Bale stoked up tensions ahead of the game by claiming England cannot match Wales' pride, as well as claiming their opponents "big themselves up before they have done anything".
Captain Wayne Rooney was diplomatic when quizzed on the remarks, but manager Roy Hodgson called them "disrespectful" and Wilshere also disagreed with the Real Madrid attacker's claims.
Asked if Bale was right, Wilshere said: "No. One thing about this team no one has ever questioned about is their pride and their passion.
"We are all representing our country and we all love England. There are a lot of young players in there as well who are in their first tournament and with that comes no fear.
"They want to show the nation what we can do and we will definitely be ready on that front. Everyone wants to play and show the manager they are ready.
"You saw that in the match and it is the same in training – the standard is really high. It is a good problem for the manager to have.
"We know Wales well – a lot of their players play in the Premier League and we have played against them previously.
"We know what their threat is – they are going to hit us on the counter-attack and obviously we know the threat of Gareth Bale - but we have to concentrate ourselves and replicate the Russia performance and be confident we can win the game.
"We played well against Russia and we are confident we can beat them."
Wilshere came on as a second-half substitute in England's 1-1 draw with Russia and says the team are pleased with how they played despite conceding a late equaliser.
Wales, meanwhile, are on a high after beating Slovakia 2-1 to lead Group B going into the clash with Hodgson's men.
Wilshere added: "We are in good place. We were disappointed, which is natural when you dominate a game like that and don't win it. But looking back we were happy with the performance.
"We played well, moved the ball around. In the past England teams have been accused of not being technically good enough and not keeping the ball, but we showed that we are good enough and can keep the ball.
"I don't think it is about bouncing back. We just need to maintain the standards we set against Russia. Of course, we need to analyse the goal and look at what went wrong there but other than that it was brilliant.
"Of course, Wales are going to be confident. They won their first game at the Euros after they haven't been to a major tournament in years. So they are going to be confident and their fans will be too.
"We are going to have to deal with that on the day but we are in a good place as well."