The coach of les Bleus was not concerned by the fact his side left it late before finally getting the better of last-16 opponents Nigeria
After struggling to find their rhythm early on, Les Bleus ultimately won through thanks to a header from Paul Pogba and an own goal from Joseph Yobo in the dying minutes.
Despite the uncertain nature of the win, Deschamps was nevertheless delighted with the outcome.
"We are part of the eight best teams in the world," he told TF1. "This is great. We will savour [it].
"We have only happiness now. I am very proud of what we have done since the start of the competition. Now we have to keep going."
Speaking about the character of the game, the former Juventus and Olympique de Marseille coach felt his team dominated in the closing stages.
"Our opponent put in a good display, like we expected," he said. "They were physically strong and we had to be ready.
"There’s always room for improvement, but we had a great finish to the game. Nigeria slowed a bit after an hour and that allowed us to create a lot of chances. We could have scored more.
"Nigeria went toe-to-toe for one hour. Maybe they tired a bit more than we did. Their attackers didn’t track back as much as we expected. This allowed us some space to play short passes and it paid off.
"I am very proud of my team, though, and to have made it to the quarter-finals. The players deserve to be here.
"We are not the best team at this World Cup, but we are doing well."
Meanwhile, he offered praise for the performance of man-of-the-match Paul Pogba, who he had previously left out of the France's second group match against Switzerland.
"It’s normal that Pogba is criticised," he said. "This is what happens in football. It will help him develop.
"He stepped up to the plate today. Maybe he kept things a bit more simple than before. All credit to him. Apart from the goal, he was very important to us. I hope he can continue to perform like this."
The only other selection quandary for the coach was whether to select Olivier Giroud over Antoine Griezmann, a decision he ultimately chose to take. The game turned when the Real Sociedad players was introduced, though Deschamps said he did not regret his initial call.
"Giroud and Griezmann are different type of players," he said. "I don’t know whether it would have worked had Antoine started. Olivier was very useful and supported Karim Benzema.
"I made a change because I wanted some more speed up front. It could have worked had I started Griezmann, but it could have gone wrong as well."
Les Bleus are in Brazil without the injured Franck Ribery but Deschamps is resigned to the fact the Ballon d'Or nominee was not ready to be part of the competition.
"It’s not that we don’t miss Ribery. Franck is and will remain one of the best players in the world. When fit, he will be here, but he wasn’t fit. I have plenty of options to pick from."
France will meet the winners of Germany and Algeria in the quarter-finals, with that encounter scheduled to take place in Sao Paolo on Friday, but Deschamps does not care who prevails.
"I wouldn’t mind playing Germany. My playing days are long behind me. What I care about is the present and the players at my disposal. We are among the final eight. We will find out our opponent shortly. We have time to prepare and we will see. I have no preference between Germany and Algeria."