After edging past the inspired Danes 2-1 in the semi-final three years ago, Gareth Southgate's men lost the final on home soil to Italy on penalties.
But they are one of the favourites to win the competition for the first time in Germany thanks to the development of Jude Bellingham, Phil Foden, Declan Rice and Bukayo Saka among others since the last Euros.
"I think England were a world class side when we met them (at Euro 2020), they got to the final of a major tournament," Schmeichel told reporters on Wednesday.
"And when you look at some of the additions and the experience they've gained they are a better side now than ever, at least in the time I've played against them. We're going to have to be on top of our game to beat them."
Denmark were left feeling aggrieved after a controversial penalty edged the semi-final three years ago England's way.
Schmeichel, though, said he is not seeking revenge.
"I'm not the kind of person to look back three years for motivation. The biggest motivation for myself is we are playing another Euros with Denmark. The biggest motivation is imagining celebrating a win for our fans after they have travelled all that way."
Denmark rode a wave of emotion three years ago after their opening game at Euro 2020 nearly ended in tragedy when Christian Eriksen suffered a cardiac arrest on the pitch.
Eriksen scored in their opening game in Germany this time round, but Denmark were held 1-1 by Slovenia to continue a disappointing run in recent years.
Kasper Hjulmand's men crashed out of the 2022 World Cup at the group stages and are at risk of another early exit should they fail to shock England.
"For me it's important that Denmark dream about achieving something big," said Hjulmand.
"Are we favourites? No. Is it a failure if we don't win the Euros? No. But we have to have the ambitions and dreams because that sets the standard. If we don't dream something is wrong."
Denmark could be handed a major boost with the return of captain Simon Kjaer after the AC Milan defender missed their opening game due to injury.
