Wilshere produced an impressive performance on his competitive debut for England in Saturday's 2-0 triumph over Wales in a Euro 2012 qualifier.
He linked up effectively with Frank Lampard and was able to get forward to good effect with Scott Parker in the holding role.
In the thick of it: Wilshere (centre) shone for England
Hart said: 'I thought Scott and Jack did really well. Jack is a class player. It's time people stopped talking about him being a good player for his age.
'He's a good player, never mind his age. The only thing to be said about his age really is that, hopefully, it means England have got him for many years to come.
'He handles everything so well and is a class player.'
Hart did not have to make a meaningful save in the 90 minutes at the Millennium Stadium as goals from Lampard and Darren Bent wrapped up the points in the first 15 minutes.
He said: 'It was a bit of a quiet game for me but the lads had virtually won the game in the first 20 minutes or so.
'They kind of killed whatever sort of buzz Wales were going to get from playing at home in the Millennium Stadium.
'The goals came at the ideal time and really kind of put a halt to anything they were going to do.
'I also felt that we had plenty left in the tank if we had needed to step up a gear.
Midfield maestro: Parker (front) transferred his impressive form for West Ham to the England side
'They have some good players who are very dangerous like Joe Ledley and Aaron Ramsey and Craig Bellamy.
'We knew they were always a threat and that's why I thought we defended really well.'
Hart added: 'We're top of the group again that's as much as you can ask. That's what we want to concentrate on doing - getting through.'
Lampard believes the midfield formation and combination was ideally suited.
He said: 'Scott carried on doing what he does for West Ham. He's been fantastic at that all season and the benefit of having an extra man in midfield showed itself.
'The three of us in there, particularly in the first half, allowed us to really get a grip of the game.
'It allows you to get a bit more forward. It allows you to get tight to their in midfield.
'We played Denmark in a friendly last month and, sometimes, when there are people behind you, you can't always commit to getting tight to their deep-lying midfield players.
'There was the bonus today of having the extra man in there to allow us to push in tight.'
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Explore more:People: Jack Wilshere, Darren Bent, Craig Bellamy, Joe Hart, Joe Ledley, Frank Lampard Places: United Kingdom, Wales, Denmark