Portugal, having lost captain Cristiano Ronaldo to injury in the first half, stunned the home crowd by winning with Eder’s strike in the second-half of extra-time.
Despite being strong favourites to win their third European title, and second on home soil, France failed to convince against Fernando Santos’s team.
And Deschamps, who captained France to World Cup glory in 1998, admitted his country was suffering after the shock defeat.
“We’ve missed a unique opportunity to win a Euros in our own country,” he said. “There are no words.
“The disappointment is there, and it’s huge, and it will take time to digest it. But we won together, we suffer together and, today, we lost together.
Portugal v France player ratings: Who impressed in Paris?
Pulled off some big saves either side of half-time to deny France. Strong under the set-piece and exceptional at close-range. 8
Got off to a shaky start, picking up an yellow card, but improved with each passing minute. Dealt with France’s pace down the flank and worked his socks off. 7
An outstanding defensive performance from the veteran centre-back. He read the game beautifully and put in some important interceptions and crunching challenges. 9
Coped with Giroud well, keeping him under wraps for much of the game. Solid throughout. 7
Came closest for Portugal before Eder’s goal with a thunderous free-kick attempt. Did a job down on the left. 7
Sat well in front of the back four and provided a constant outlet for the defence throughout the game. 7
After impressing earlier on in the tournament, Sanches failed to live up to expectation. He flashed with the occasional moment of brilliance but it wasn’t his best game. 6
Quiet at times. He neither impressed nor made any glaring mistakes. 6
Pulled the strings for Portugal in the centre of the park with his short ball work and created a number of chances. 7
Started slow but ended the game well. Brought variation to his game, which caused a lot of trouble for the French defence, and worked hard for those balls in behind. 7
An injury in the 25th minute brought an early end to his game. N/A
Best of the bench – Eder
Super sub. Challenged well at the corners, ran hard, and scored the all-important winning goal. What a night to remember. 8
A strong performance between the sticks. Denied Portugal’s early chances with his quick reactions but caught off-guard for Portugal’s goal. 6
Battled well in the first half to keep Sanches at bay. Seemed to disappear somewhat in the second half. 6
Tracked back well, put in some important interceptions and made a series of huge challenges within his final third. Reliable throughout but ultimately unlucky. 7
Caught napping early on to gift Nani a dangerous chance on goal. Conceded too many fouls too. 6
Like Sagna, he enjoyed a strong first half and used his strength well in challenges. Had less of a say in the second 45 minutes. 6
He’s been hit-and-miss all tournament and this game summed it up. He threatened with moments of magic but often went missing. Not his day. 6
Defensively solid but just couldn’t get a grasp of the game. 6
France’s stand-out player. He brought urgency to the French game with his surging runs and was genuinely world class at times. Threatened with some dangerous shots. 8
After such an impressive tournament, he struggled to deliver tonight. He provided little threat on the ball and his set-piece game was off the mark. 5
Forced Ronaldo off with a strong early challenge but he was another player who failed to live up to expectation. 5
Offered very little going forward. A dead weight up top. 4
Best of the bench – Andre-Pierre Gignac
Claim close to settling it for France in the 93rd minute and was very lively in front of goal, creating a number of chances for himself. 7
“We so wanted to rouse the French people, and it would have been magnificent to bring the trophy home to them. But, unfortunately, that isn’t going to be the case.”
France faced Portugal just 72 hours after defeating Germany in a draining semi-final in Marseille and Deschamps hinted at his players being fatigued by that victory.
“Even if we were a little bit tired as well, that’s not an excuse,” he said. “We had chances to score, and the last one fell to ‘Dédé’ Gignac.
“It came down to tiny details, it was a close match. We had chances, as did the Portuguese, but unfortunately they scored.
“It’s a great disappointment for it to end now, with this final.
“We must not throw everything that we’ve done away, but we threw away a great chance to be European Champions – not the only one, but a great one.”
Portugal’s victory perhaps carried even greater weight with the success coming with Ronaldo sat on the sidelines, nursing the knee injured in a challenge by Dimitri Payet.
Pepe, the Real Madrid defender, admitted Portugal were forced to dig deep to overcome France and win the country’s first major title.
“This was tough because we lost our main man, and we’d pinned all our hopes on him,” Pepe said. “He’s a player who can score a goal at any second.
“You know his abilities. But when he said he couldn’t go on, I told my team-mates that we had to win it for him. That we were going to fight, to fight for him.
“At the break, the manager surprised everyone. He set us up very well, strategically speaking. This was Plan B, I guess, because he moved the team around very well.
“The substitutes came on at the right time and the right players each time, and we put blood, sweat and tears on the pitch.
“I said we’d leave it all on the pitch for our people, for our nation, and that’s what we did.
“We worked so hard and, thankfully, we managed to secure a positive result.”
Eder, who endured an unsuccessful loan spell at Swansea City, claimed Ronaldo acted as inspiration for his goal.
“Ronaldo told me I would score the winning goal for the team,” the striker told O Jogo. “He gave me this strength, this energy and it was vital.
“It was a goal I’ve been working for from the first minute of the Euros.
“For all the work we did, for all of the Portuguese, it’s fantastic,” he added. “It’s well deserved and we should all be congratulated.”
Meanwhile, France captain Hugo Lloris, who produced a stunning save from Ricardo Quaresma in normal time, praised Portugal for their victory, despite their defensive approach to the game.
“Credit to Portugal,” Lloris said. “They didn’t necessarily play positive football over the tournament, and they only won one match in 90 minutes, but it showed great strength of character for them to win this.
“We had to be more clinical. When you hit the post in the dying seconds, football can be very cruel.
“But you have to get on with it. We’ll have to digest things, but the overriding emotion now is one of sadness.
“We have to learn from this and keep going forward.”