Spain had taken the lead when Mikel Oyarzabal fired in a low strike in the 64th minute.
Only three days ago, world champions France came from 2-0 down to beat Belgium 3-2 in the semi-final.
“I’m very proud and very happy for the players,” Deschamps said.
“We went behind in both our matches. Today we equalised quickly after going behind. Beyond the talent that we have in this team, there’s also their character and mentality.
“In the second half we were more aggressive and forced them into mistakes.”
Spain boss Luis Enrique said Benzema’s brilliance turned the game, with the Real Madrid veteran’s strike hitting the top corner.
“The unfairness of football is that we had the chance to put a knockout move on France when we went 1-0 up but Karim Benzema did something superb,” Luis Enrique said.
Benzema, who came back from international exile prior to Euro 2020, was delighted with his moment of magic.
“Usually in such positions, I try to cut in and shoot low,” he said. “When you score a goal like that there’s always an element of luck.
“I knew from the moment it left my boot that it was going in, but not that it would find the top corner.”