Bronze reveals England 'are not happy' with their World Cup performances
The fourth-ranked Lionesses survived a scare in Monday's round-of-16 penalty shootout win over a Nigerian side who gave England fits all night.
"We can give more," Bronze told reporters. "We're a fantastic team with highly talented players.
"There's no point in playing our best performances in the first games, we might as well save them for the quarter-finals or further than that."
The Lionesses will be without Lauren James, their leading scorer with three goals, in Saturday's knockout game after she picked up a red card for a stamp to the backside of Nigeria's Michelle Alozie.
The Chelsea striker, who issued an apology, could sit out longer pending a FIFA disciplinary review.
"The most important thing is that we're coming out of games with wins," Bronze said.
"We're the ones who are still in the competition and there's many top teams who are going home because they haven't been able to get that point or been able to see the games out in the penalty shootout and we have.
"We've shown that side of our team that we know what it takes to win."
Coach Sarina Wiegman said after the Nigeria win she had never experienced so many problems in a game or tournament, with the team also losing midfielder Keira Walsh for a game-and-a-half to injury.
Bronze, a defender for Barcelona, praised her squad's resilience.
"We've built on every game, we've taken something from every game - whether that was the Haiti game that was physical, the Denmark game when we lost our key player in Keira, the China game we changed the formation completely, (and) we had a red card," she said.
"Everything that has been thrown at us, we've dealt with and moved forward. I don't see many other teams who've had that adversity and if they had, I don't think they've managed to overcome the way we have.
"At the same time, we are not happy with our performances."
