Samuel Umtiti's 51st-minute header at St Petersburg Stadium sent the French into the final, where they will be seeking their second win since 1998 - when Deschamps captained them on home soil.
"It was exceptional," Deschamps said in a pitch-side interview. "I'm very happy for my players, we showed character and the right mentality, it was very hard for us tonight. We worked hard defensively.
Deschamps, who is aiming to join Germany's Franz Beckenbauer and Brazil's Mario Zagallo as the only men to have won the World Cup as both a player and a manager, added: "We had to take advantage a bit more in the counter attacks. but congratulations to my players and my staff. I feel very proud for my group.
Samuel Umtiti (right) was the match-winner in St Petersburg
Image credit: Getty Images
"Forty-nine days together, it is a lot of things, difficult things, the group stage, it is the merit of everyone. We don’t realise the support we’re receiving like we did at the European Championships.
France reached the World Cup final 20 years ago after a semi-final victory was sealed by a Lilian Thuram header against Croatia, and Deschamps was asked if he felt Umtiti's goal from similar circumstances was a sign of destiny for his side.
“I feel that everyone has their own destiny," he replied. "We always try to find comparisons, rightly or wrongly. We always have to give credit to the players.
“We have four days to share this happiness with our families and we will come back tomorrow calmly and see who is going to face us. We will do everything it takes to ensure we are on the right side this time, and not repeat what happened two years ago."
Goalscorer Umtiti said the win had come on the back of the work of the entire team.
"A lot of pride," said the defender. "We worked hard... I scored but we delivered a good match and I'm very proud of everyone. They worked in '98 and we worked today, we reached out target to get to the final, I'm very satisfied."