Gerrard provided the assist as the returning Wayne Rooney headed home from point-blank range for the winner just after half-time and he feels an unheralded squad can continue to improve.
England now face Italy in the quarter-finals on Sunday.
He told ITV1: "It was a difficult group and the idea was to try and win it. No-one believed in us at the start but we're gaining momentum at the right time.
"I don't think tonight's performance was fantastic, but we stuck together, got the job done and won 1-0 against a good team.
"We've been criticised in the past maybe for not turning up, under-performing and we can take that, we're man enough. But you saw a reaction.
"When you get criticised it's not nice and you have to react by playing better and I think that's what we did."