Having fallen behind to an early Robbie Brady penalty, the hosts struggled in the first half, heading into the break 1-0 down.
An Antoine Griezmann double eventually secured the win for France, and Deschamps reflected on a tough afternoon where his side were required to show their character.
"I knew that this match was going to be difficult and when Ireland took the lead it made us a little bit more uncomfortable in the first half," the 47-year-old said.
"We did react well later on. There was a lot of enthusiasm from them. We really had to dig deep to get through this situation, to equalise and then to take the lead."
With late goals to secure victories against Romania and Albania in the group stages, France have garnered a reputation for overcoming adversity in this tournament.
However, Deschamps insisted he does not want to make it a habit, and these testing situations stem from a tight competition.
"We don't do everything really well," he added. "I've not seen any team who does everything really well. It's complicated for all the teams.
"It's a very balanced European Championship.
"The French team with all our players are not going to stop them and slow them down. I wanted to provide stability in defence. I didn't want to stop our attackers.
"This team is bringing emotion to the crowd and making people fall in love with them. We really needed the great support we had from the fans."