Had Everton’s players been at 100% rather than “70% physically”, as new manager Koeman suggested pre-match, then perhaps the outcome at Goodison Park would have been different.
The Toffees gave Tottenham barely any time on the ball in the opening period with their incessant pressing.
This style of football, seen under the Dutchman when he was at Southampton, has quickly been incorporated at his new club.
Young Spaniard Gerard Deulofeu, the lone man in attack with Romelu Lukaku injured, led by example as he badgered the Tottenham centre-backs Toby Aldeweireld and Jan Vertonghen when they had the ball.
Everton’s goal came from a set-piece and Lloris might be disappointed that neither he nor his defence dealt with it, as Barkley’s teasing ball in from out wide missed the heads it was intended for and bounced in beyond the reach of the France international.
The Spurs keeper did not appear to be struggling up until that point but came off 10 minutes before half-time with a hamstring problem.
The right change at the right time
Tottenham’s England striker Harry Kane was playing at Goodison Park – although you would be forgiven for not noticing.
He played a lone attacking role for 56 minutes and hardly had a sniff of the ball, which was partly due to poor service and partly due to brilliant closing down by Everton.
It was a similar story for attacking midfielders Dele Alli and Christian Eriksen, who at least managed a shot on goal in the first half.
Manager Mauricio Pochettino finally decided to twist 11 minutes into the second half when he brought on new forward signing Vincent Janssen to support Kane. What that did was pull one of the Everton midfielders further forward and freed up more space in the middle third.
Kyle Walker exploited this new-found freedom in the 59th minute when he surged down the right and delivered a brilliant cross for Lamela who nodded in from close range.
Spurs should have won the game but were denied by two outstanding saves by Everton’s new goalkeeper Maarten Stekelenburg.
How did the new signings do?
Idrissa Gueye – An absolute terrier in defensive midfield for Everton. A brilliant lunging dive in front of Alli in the second half which caused the England midfielder to rush his strike was a great example of his tenacity.
Maarten Stekelenburg – The Dutchman had a quiet game until the second half when he produced two tremendous saves. A one-handed stop denied Janssen at point-blank range and then he tipped over Lamela’s deflected shot.
Victor Wanyama – Similar to Gueye, in the sense the former Southampton player made his presence on the field known early on with a couple of challenges.
Vincent Janssen – His arrival on the pitch sparked a change in fortunes for Spurs and he was unlucky not to score. All in all, a good start to his Premier League career.
Man of the match – Idrissa Gueye (Everton)
What the managers said
Tottenham manager Mauricio Pochettino: “The first half was difficult for us and we did not play well. Hugo Lloris got injured and that was a big impact on us. In the second half we played as we usually play.
“They scored early and they believed they could win the game. They were very motivated.
“Lloris has a hamstring injury and we need to assess tomorrow to see what happens.
“We tried to correct the problems we had in the first half. With another striker, the team felt comfortable. Vincent Janssen brought good energy on the team and he gives us a different option.”
On transfers: “We may get one or two. We are very open, it is not easy to bring in players who can help us but we are trying.”
Everton boss Ronald Koeman:
“We had a big, big chance close to half-time with Gerard Deulofeu. They had two big chances too but I think it is a fair result.
“The reaction of the crowd and fans was fantastic. I am very pleased about our first performance against a very good team.
“Ross Barkley’s first goal is one of his qualities. I want the players to work hard and the pressing starts from the strikers. The players need to improve in that.
“One save from Maarten Stekelenburg was incredible in a key moment of the game.”
On transfers: “I was focused on today’s match but we are waiting for two or three new players and the board are working hard to bring them in. I don’t talk about names. I hope we can sign two players next week.”
The stats you need to know
Barkley has scored in each of his last three Premier League appearances on the opening matchday for Everton (2013-14, 2015-16 and 2016-17).
Gareth Barry has now appeared in his 20th Premier League season – only Ryan Giggs (22) has played in more, and only Rio Ferdinand and Frank Lampard (20) have played in as many.
Everton have drawn their last four opening day matches, with Barkley scoring three of their seven goals in this run.
Lamela has had a hand in seven goals in his last seven Premier League appearances (three goals, four assists).
Everton have not defeated Tottenham in any of their last eight Premier League meetings.
Kane had fewer touches than any other Tottenham outfield player to start versus Everton (35).
Everton are away at West Brom at 15:00 BST next Saturday and Spurs host Crystal Palace at the same time in their first league game at White Hart Lane this season.
Match ends, Everton 1, Tottenham Hotspur 1.
Second Half ends, Everton 1, Tottenham Hotspur 1.
Attempt missed. Erik Lamela (Tottenham Hotspur) right footed shot from the centre of the box misses to the left. Assisted by Kyle Walker with a cross.
Corner, Tottenham Hotspur. Conceded by James McCarthy.
Attempt blocked. Vincent Janssen (Tottenham Hotspur) left footed shot from the right side of the box is blocked. Assisted by Christian Eriksen.
Substitution, Everton. Tom Cleverley replaces Gareth Barry.
Foul by Vincent Janssen (Tottenham Hotspur).
Mason Holgate (Everton) wins a free kick in the defensive half.
Attempt blocked. Danny Rose (Tottenham Hotspur) left footed shot from the left side of the box is blocked.
Corner, Tottenham Hotspur. Conceded by Maarten Stekelenburg.
Attempt saved. Erik Lamela (Tottenham Hotspur) left footed shot from the left side of the box is saved in the centre of the goal. Assisted by Harry Kane.
Attempt missed. Christian Eriksen (Tottenham Hotspur) right footed shot from outside the box is just a bit too high from a direct free kick.
Danny Rose (Tottenham Hotspur) wins a free kick in the attacking half.
Foul by Gareth Barry (Everton).
Corner, Tottenham Hotspur. Conceded by Ramiro Funes Mori.
Attempt saved. Vincent Janssen (Tottenham Hotspur) left footed shot from the centre of the box is saved in the bottom right corner.
Attempt blocked. Danny Rose (Tottenham Hotspur) left footed shot from outside the box is blocked.
Corner, Tottenham Hotspur. Conceded by Maarten Stekelenburg.
Substitution, Everton. Aaron Lennon replaces Kevin Mirallas.
Attempt missed. Ross Barkley (Everton) right footed shot from outside the box misses to the right. Assisted by Arouna Koné.
Foul by Kyle Walker (Tottenham Hotspur).
Ramiro Funes Mori (Everton) wins a free kick on the left wing.
Foul by Erik Lamela (Tottenham Hotspur).
James McCarthy (Everton) wins a free kick in the defensive half.
Attempt missed. Ramiro Funes Mori (Everton) left footed shot from outside the box misses to the right. Assisted by Gareth Barry.
Corner, Tottenham Hotspur. Conceded by Mason Holgate.
Vincent Janssen (Tottenham Hotspur) wins a free kick on the right wing.