Les Bleus crashed out at the quarter-final stage following a 1-0 defeat to Germany, with Mats Hummels scoring the only goal with a 13th-minute header.
It may have been a different story had Karim Benzema not squandered numerous half-chances, leaving Deschamps to reflect on what might have been.
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"Towards the end we were exposed and they could have scored a second. The players are frustrated."
Deschamps has no intention of quitting his post, however, and confirmed he would stay on to build for the European Championship on home soil in two years' time.
"I definitely hope so, the squad was born during the return leg [of the play-off] against Ukraine and during the warm-up games we did well," he added.
"We are not as experienced as Germany but I am proud of what we have done on the pitch and behind the scenes. I know I have a lot of work to do but it's promising. We would love to keep the momentum and keep the quality of the team. Although I'm disappointed there are a lot of positive things happening with this team.
"Everyone was sad and frustrated afterwards and I can't get that away from that as I feel the same way. But let's not forget what we have done. We wanted to go further but I don't think there was a huge gap between the sides."
Deschamps, a World Cup winner as a player in 1998, refused to criticise Benzema but admitted his side were not clinical enough in front of goal.
"Sometimes you need a bit of luck on your side, or to be a bit faster," he said.
"Also [Germany goalkeeper Manuel] Neuer made some good saves. This is the highest level of football, we had chances, but unfortunately we were not as efficient or as lucky as we could have been.
"Karim had one or two chances. He didn't score but I don't think he needed much, that little bit extra you need to score a goal was not on our side."