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The British rivals meet in Group B at Euro 2016 on Thursday (14:00 BST).
Last week, 26-year-old Bale said the Welsh had more passion and pride than England, who "big themselves up before they've done anything".
"I've been in the game sufficiently long to know every opponent has got an opinion," said Hodgson.
"The other day it was [Russia goalkeeper] Igor Akinfeev saying we were the worst seeded team and now it's Gareth Bale.
"They can have those opinions but I don't have any doubts personally about our patriotism or desire and that's the important thing.
"I would recommend anybody who does have any doubts about players in that respect to watch the game [against Russia] and come to me afterwards and show me where they've seen that lack of passion and lack of patriotism because I certainly didn't see it.
"We know who we are, we know what we are. We don't have any doubts about ourselves in that respect."
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England started their campaign with a 1-1 draw against Russia, while Wales beat Slovakia 2-1 in the their first game in a major tournament for 58 years.
It was Bale who scored Wales' opener in Bordeaux, and England captain Wayne Rooney is aware of the threat posed by the Real Madrid forward.
"I think he is a fantastic player, probably in the top five players in the world," said the Manchester United skipper.
"He is the biggest threat for Wales, but I don't think we will go out and man-mark him.
"I think we have to go out and play our game. They will have a lot to think about our team, too. I'm sure it will be a fascinating game."
England were leading 1-0 against Russia thanks to an Eric Dier free-kick but they had to settle for a 1-1 draw after conceding an injury-time equaliser.
The result means they have failed to win any of their last five matches at major tournaments, but striker Harry Kane insisted England fans should remain positive.
"We have got great players, we ain't no mugs," said the Tottenham forward. "We are more than confident. We are not going to let this affect us.
"On another day it could have been three or four nil. We limited Russia to very few chances and we had plenty. We have got to learn from it, take the positives and prepare for Thursday."
Manager Roy Hodgson says he does not doubt England's "patriotism or desire", in the wake of comments made by Wales striker Gareth Bale.