The 32-year-old led England to a 1-1 draw against France in Donetsk after Joleon Lescott’s opener was cancelled out by Samir Nasri’s superb strike from 20 yards in the 39th minute.
In the other group game, Andriy Shevchenko’s double inspired co-hosts Ukraine to a 2-1 victory over Sweden, leaving England level with France on a point.
Next up for Roy Hodgson’s side is a tricky encounter against Sweden on Friday, and Gerrard wants England to capitalise on their positive start to the European championship by claiming three points against Erik Hamrén’s side.
“We would have been delighted with a win but France have got fantastic players,” said the England captain.
“I thought 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. Now we need to follow it up with a win and try to get four points out of two games.
“This is only a good point if we go on to get the points we need to get out of this group.
“We will analyse this game – what we’ve done right and what we’ve done wrong – and then we’ll go into the Sweden game hopefully all recovered. There’s still loads of hard work to do.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news