"Whatever's going on around England, there's a lot expected of them because they've had great players down the years," Coleman told journalists on Wednesday.
"There's a lot more pressure and expectancy on the England boys than on us but the expectancy and the pressure come from within our group, we expect ourselves to compete against the best."
England need a positive result after conceding a late equaliser in their opener against Russia, while Wales, who beat Slovakia 2-1 on Saturday, could qualify for the round of 16 with another win.
Wales forward Gareth Bale has suggested that his side have more national pride than their English counterparts, a line which was dismissed by England manager Roy Hodgson in his pre-match news conference.
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Coleman also played down the comments, saying: "If one of ours has said something that one or two of the England boys don't like, it's irrelevant. When the whistle goes tomorrow, we'll see who's ready."
Rivalry between the two sides was always going to create an atmosphere, Coleman suggested. "England came out of the hat and we didn't want that. We didn't want the circus that comes with England."
(Reporting by Ed Dove; editing by Clare Fallon)
