The Three Lions' skipper provided the cross for Andy Carroll's towering header which opened the scoring in Friday's clash with Sweden, but England were punished for their lack of concentration when confusion from set-pieces allowed their opponents to steal two goals.
Roy Hodgson's men rallied and managed to edge back in front thanks to goals from Theo Walcott and Danny Welbeck to claim a vital three points, but Gerrard says the defensive cracks must be addressed.
"It was very eventful, but it was important that we got over the line and got the three points tonight," Gerrard told the Football Association's website.
"There were mistakes in the game, I thought we were very sloppy at set pieces. When you take the lead in international football it's important that you stay solid and don't make mistakes. We made it really difficult tonight, but I'm pleased with the win.
"I think we've proved that we can be ambitious and we can be bold at the right times, but we paid for a lack of concentration at set-pieces.
"People who know the game will tell you that you go out of competitions and lose big games if you concede goals at set-pieces.
"That was the only disappointment of tonight, I think general play we were better than Sweden, we played the better football and created a lot more than them."
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"If you give him the right service he'll get you goals, he's proved that in his career," Gerrard explained.
"You don't always get them right, but I got tonight's cross right. There was still a lot of work to do, it was a fantastic header."
England welcome back Wayne Rooney after his two-match suspension for the match against Ukraine and Gerrard believes the Manchester United star can provide the team with "that little bit extra".
"He's itching, he's ready to go," Gerrard added. "That's another big boost, that we've taken four points from two games. We've got Wayne to come back in, he's fresh and hopefully now he can provide that little bit extra that we need."