The 26-year-old Hart will start this summer's World Cup in Brazil as Roy Hodgson's first-choice as the Three Lions look to navigate out of a difficult group which includes Italy, Uruguay and Costa Rica.
Hart started every one of England's qualifiers for the tournament, despite losing his place in the City side to Costel Pantimillon following a dip in form.
England's record cap-holder and former captain Shilton lined up in goal for his country on 125 occasions, and believes those weeks spent on the bench at the Etihad Stadium prove Hart is not yet ready to be spoken of in the same breath as the likes of Germany's Manuel Neuer or Gianluigi Buffon of Italy.
"I don't think he is quite at the top at the moment because he is still young and, as we have seen this season, he is prone to mistakes," Shilton told Press Association Sport.
"At the moment he has been making too many errors, especially when he eventually fell out of City's side during a crucial period.
"At the same time he has a lot of natural ability and I like his confidence, and he gives that confidence to the defence as well.
"He still has a lot of improvement in him. When he has a couple of consistent years, you could start to say he is up there with the best in the world."
With three goalkeeper berths making up England's 23-man squad for Brazil, Hodgson has to make a decision on who his two back-up choices will be.
West Brom's Ben Foster is likely to take one place while Fraser Forster of Celtic and Norwich keeper John Ruddy appear to be vying for the final spot.
That trio have just eight caps between them, compared to Hart's 39, and whichever two make the cut Shilton is worried they do not have the international experience to seamlessly step in if required.
"There have not been a lot of games for the kids underneath Hart," he said.
"I think between now and the World Cup, Roy will look for the time to give full matches to them, just to get them in the routine of playing for England.
"There is not much time now, Roy has to start playing what he considers to be his best team. It is a worry but I think he will give Ben Foster a full game and he is good enough to start keeping Joe on his toes. Hopefully that will create more competition."
:: With 125 appearances, Peter Shilton is England's most capped football player. Celebrating the launch of the Wasgij Original 21 Football Fever jigsaw puzzle, Jumbo Games is running a promotion offering the chance to watch England take on Uruguay alongside Shilton on 19 June 2014.