Joleon Lescott headed 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 and fell deep into their own territory, 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,” said Gerrard.
“We caused them as many problems as they caused us so we’re satisfied with the performance”
Steven Gerrard Quotes of the week
“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 player 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,” said Gerrard.
“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.”