England have failed to overcome the Swedes in seven previous World Cup or European Championship encounters ahead of the Group D clash in Kiev.
But Gerrard is adamant that sequence should end, even allowing for the threat posed by Swedish striker Zlatan Ibrahimovic.
Gerrard said: "I would think the same level of performance against France will be good enough to beat Sweden.
"I would say so with all due respect to Sweden who are a good, strong team, but they are not France.
"I think we can be a little bit more bold and a little bit more ambitious and get at the Swedes a little bit more.
"We are confident if we reach the same level of performance, it will be enough for a victory."
However, Gerrard warned: "Although we are confident, that's not to say we won't be trying to learn from the mistakes we made in the first game.
"We've analysed what we did right and wrong against France and we will be trying to improve on our performance as well.
"I'm really happy with the start we've made to the tournament. It was really solid and we've left ourselves a good platform to build on.
"The boys are confident we will be on four points after this next game and that will be a good start to this group."
Gerrard knows England have to counter the danger of Ibrahimovic if they are to inflict upon Sweden their second defeat of the tournament.
He said: "Ibrahimovic is a world-class talent and he is very dangerous so we need the same level of commitment defensively to try and stop him.
"If you give him time and space, he can hurt any team and we are well aware of him.
"We've watched videos of him and we are going to watch some more so we are going to be well prepared for Ibrahimovic.
"But he is not the only good player Sweden have. We have to worry about them as a whole team.
"They get dangerous crosses into the box, they are a big side. There is a lot more threat from Sweden than Ibrahimovic but he is a world-class talent."
Gerrard knows the qualities England have to counter to get the better of Sweden, who were beaten 2-1 by Ukraine on Monday.
He said: "People say 'why can't we beat Sweden?' and that is credit to Sweden.
"They never give up, they fight to the end. Hopefully it will be different tomorrow [Friday] because we are very confident we can beat them."
England manager Roy Hodgson is relishing the contest against the country where he built his reputation as a coach, leading Halmstad to two league titles and Malmo to five in a row.
He said: "I've faced Sweden many times, three with Switzerland and once with Finland, and I've managed to achieve two victories and two draws.
"But this is the most important occasion for me."
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Hodgson has called for England to be more "clinical" with their attacking play.
England earned plenty of praise for the defensive qualities against France in Donetsk but they failed to make the most of the few opportunities that came their way on the counter-attack and had to rely on Joleon Lescott's header from a set-piece move to score their only goal.
Hodgson said: "I was happy with the start. We played quite well, certain aspects of our game were good.
"We must maintain that and, if we are going to win matches, we've got to continue to work hard on the attacking side of the game.
"We have to try to make certain when we do get these good counter-attacking opportunities that we maximise them and take advantage to the full.
"When we win the ball back and break out, we've got to make certain the last pass, cross or actual finish is very clinical.
"It is hard to get good goal chances at this level of football. You are not going to get many during the course of a game and you have to be very effective when the chances come your way.
"I am not talking about the clear-cut one-versus-ones with the keeper but the situations where you've got behind the defence and it's a question of making sure the last pass gives someone the chance to score a goal.
"That is something we've been working on consistently."