Attila Fiola's strike just before half-time put the hosts, who were backed by a raucous crowd of around 61,000 spectators, on course for a famous European Championship victory.
France squandered a number of chances before that opening goal and hit the post through substitute Ousmane Dembele, but they did eventually find a way through.
France would have booked a place in the knockout stages with a victory, but their failure to find a winner means that the world champions are left waiting on their last-16 spot.
Hungary frustrated Portugal before ultimately losing 3-0 earlier this week and Deschamps insists there is no shame in being held by a side ranked 37th in the world.
"Hungary put on the match of their lives. Good for them," Deschamps told beIN SPORTS.
"We had chances in the first half and found ourselves behind to their only opportunity. They had a lot of support and that clearly gave them strength.
"They defended really well, as they did against Portugal until late on. It's a point. It's not what we hoped for but given the context, we will take it anyway."
France beat Germany 1-0 in their opening Group F game and still have Portugal to face in the final round of fixtures next week.
"It is an important point today because it leaves the cards in our hands for the last game," Deschamps added.
"There are things to improve and I knew we were not going to crush every team, even after playing a good game and beating Germany.
"Our objective is to qualify for the next round and we've still got a bit of leeway with our four points, even though we'd have liked to come out of this game with six."
Asked if changes will be made for that showdown with fellow heavyweights and reigning European champions Portugal, Deschamps gave little away.
"Maybe," he said. "The next game will be important. I might shake things up as fresh legs can be important. With the temperature as high as it was today, it was very difficult."
Dembele looked lively after being brought on shortly before the hour mark, but he was replaced by Thomas Lemar just 30 minutes later.
He was holding the back of his leg when leaving the field and Deschamps has confirmed the Barcelona forward sustained another injury.
"It's a blow to his tendon, behind the knee," Deschamps said at his post-match news conference. "We will have to check, but he was in enough discomfort to come off."
France are unbeaten in nine matches at major tournaments, although Saturday's draw ended their five-match winning run at such competitions.
It is the first time Hungary have avoided defeat to France in any competition since May 1976, ending a five-game losing run against Les Bleus.
The Magyars are still in with a shot of advancing from Group F with a trip to Germany to come and head coach Marco Rossi is delighted by the effort put in by his players so far.
"I can only thank the team," Rossi told M4 Sport. "They played an exceedingly good tactical match and carried out their business with the correct amount of bravery and heart.
"Nowadays, many coaches are convinced that the team wins because of the coach's tactics. They're wrong. The players are always the lead characters. Today they performed.
"We knew there would be difficult moments during the match, when things didn't go as we wanted, but we're working to cope with those.
"We possess players who are committed and work hard every day to improve themselves. We have our limits, but it really augurs well for the future."