Ronald Koeman praised his players for answering the ‘mental question’ posed by Tottenham after holding the North London club to a 1-1 draw at Goodison Park on the opening day of the Premier League season.
The Merseyside outfit impressed with a lively, organised display in a first half that saw Ross Barkley's fifth-minute free-kick give them the lead and Gerard Deulofeu's attempt to add a second in the closing stages thwarted by Michel Vorm.
But having offered little, Spurs then snatched an equaliser just before the hour mark via Erik Lamela's header, and the visitors almost won it late on, with two superb saves by Maarten Stekelenburg keeping out a shot from substitute Vincent Janssen and a deflected Lamela strike.
Koeman, who is looking to rejuvenate Everton after leaving Southampton in June to succeed Roberto Martinez, said : "I am happy about the team performance.
"I think the first 45 minutes was really excellent. We had good team organisation, we put a lot of energy in, and we were very dangerous up front.
"We had a big opportunity before half-time to score a second goal, and if we take that then it's a different game. Being one or two goals up is a completely different situation.
"We knew it would be difficult towards the end because they have really good players, scoring players. Of course they had two big opportunities, and they were great saves by Maarten Stekelenburg.
"That was important for us to keep the result, because it is also a mental question."
He added: "We showed what we like to see, and you could see the reaction of the fans, really supporting the team, and that is good. Overall we worked very hard.
"This is the first game and I am happy overall."
Everton were without their top-scorer from last season Romelu Lukaku, who injured his heel a week earlier in a friendly and has been linked with a big-money move away from the club.
Koeman emphasised post-match that Lukaku had missed out due to injury and indicated a return to the team was on the cards for next Saturday's trip to West Brom.
"If he is fit then he will start. That was not an issue today, he was not fit enough," Koeman said.
"Next week? Yes, normally he would be fit for that."