Joleon Lescott nodded home the opener in the 31st minute only for Samir Nasri to beat Joe Hart at the near post with a fine strike nine minutes later.
England tired in the second half, but they held France out to secure a point from their Group D opener.
"We would have been delighted with a win but as you saw tonight France have got fantastic players," Gerrard told ITV1.
"We caused them as many problems as they caused us so we're satisfied with the performance.
"But we said before the game that win, lose or draw we wouldn't get carried away and that this was just a platform.
"It's great to get off the mark points-wise."
Gerrard was impressed by the performance of 18-year-old Arsenal winger Alex Oxlade-Chamberlain, who was preferred ahead of Stewart Downing on the left flank.
"They're young players but good players. Wayne Rooney showed all those years ago that if you're good enough, you're old enough," Gerrard said.
"Oxlade-Chamberlain showed tonight that he's good enough for this level.
"He's still got a lot of learning to do, but playing with experienced players he'll get there."
England coach Roy Hodgson was pleased with his side's defensive performance and felt they could have taken all three points.
"France don't panic in the final third so you have to be very disciplined in your defending," he said.
"To finish 1-1 and ask the questions of them that we did, I've got to be happy.
"We kept them at bay and there weren't that many situations in front of our goal where I was panicking in any way.
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"And there were a few situations in their third where we would have scored a second goal with a bit of luck."
Hodgson refused to criticise the display of referee Nicola Rizzoli.
"The referee did OK. It's foolish to start commenting on the referee's performance," he said.
"Sometimes you'll get a bit of luck, sometimes not.
"I know that Steven (Gerrard) was aggrieved not to get a free-kick, but the referee was fair to both sides. It wasn't one-sided."
England face Sweden on Friday but Hodgson, who reported a clean bill of health from the game, admitted the toughest opponents of Group D had been negotiated.
"France are one of the favourites in the group," he said.
"They'd gone 21 games unbeaten before today and people were tipping them to be potential winners of the tournament.
"We can't deny on paper they might be the hardest game, but I've got a lot of respect for Sweden and the Ukraine.
"I've got to be very proud of that performance. Maybe that final ball needs to improve and we were maybe a bit anxious in the final third.
"But there were good signs of a team wanting to do well."
Hart was pleased with the way England had begun Euro 2012 and paid tribute to Nasri for his goal.
"Samir's a clever player, we dropped off a little bit. It was a good goal and we have to concentrate on the good performance," Hart said.
"You can question the team all you want, but you'll always get belief, pride and quality.
"People forget that we're England and we're a good side. In that first 25 minutes they weren't ready for us."
England did suffer a blow though as Hodgson confirmed goalkeeping coach Ray Clemence had snapped an Achilles tendon and would be returning home.
Nasri, who was voted man of the match, added: "It is a big honour but I would have preferred to win the game. We didn't lose and that is the important thing.
"I am confident about our possibilities of going through to the quarter-final."
Of the goal, he said: "(Franck) Ribery gave me the ball back and the England defence was really low (sitting back). Joe Hart knows I open my body up so I did the opposite."