It took until the 85th minute before France finally made the breakthrough with a shot from substitute Randal Kolo Muani which was deflected by defender Jan Vertonghen for an own goal.
"We made a lot of progress and I think that the opponent was obviously a little bit more cautious even though on paper Belgium is quite an offensive team," Deschamps said.
"They are quite an attacking team, they maybe held back a little bit more than we're used to seeing. On our side as well, even though we did everything we could to try and attack, to try and score, to try and create chances.
"We managed to create more chances than Belgium did, but we were also maybe on the back foot. We were intelligent, we were playing the waiting game and we weren't going to fall into the trap of giving them the space that they were looking for."
The France coach was happy with his side's performance, and how they dominated possession, but wanted to see more attempts on goal from a team which has yet to score from open play at the Euros, with a penalty and two own goals.
"We have the ability to have a hand or have a better hand over our matches and to keep ball possession. This is something that I enjoyed this evening," said Deschamps.
"Obviously you can't win games just through possession, but it's better having the possession of the ball and attacking and making the team defend. But the number of shots we had, that's probably the only thing that I want to work on.
"I think that on the pitch there's high intensity, and even if today the goal is enough for us to get to the quarter-finals, we've always got the capacity and the capability to score more."
France came into the tournament as one of the favourites to win the Euros and, despite the fact that they have failed to overly impress so far, Deschamps does not want anyone taking the fact they are still involved for granted.
"I'm immensely proud of what we've been able to do and we're into the quarter-finals and that's probably what counts," he said.
"Even though people expect us to get to the quarter-finals, let's not play this down, let's savour the moment.
"What I've said to my staff here is that we wanted to savour the moment, we should appreciate every moment. Nothing comes at the blink of an eye or in a click of your fingers and we're in the quarter-finals."