Even Fabio Capello admitted in the aftermath of last week's friendly defeat to France that he could not wait to pair Carroll up with Wayne Rooney, who should be available for a February friendly, possibly against World Cup semi-finalists Uruguay.
However, Butt does not feel Carroll should have to live with such lofty expectations at such an early stage of his career.
"It is a bit harsh on Andy," the former Newcastle skipper said.
"He has only been playing for two years and one of those was in the Championship. To put all that pressure on him is unfair. It can damage young players.
"There are a lot of players who could be the perfect partner for Rooney.
"Andy is just starting his career. All eyes are on him. Hopefully it will die down for him, get on with his football and keep out of the press."
Butt may have found places to escape in Manchester, and would surely find them in Hong Kong should he, as expected, confirm a three-month post-New Year stint with South China.
Newcastle is a slightly harder place to avoid attention.
"It really is a goldfish bowl," said Butt. "The supporters are so passionate it is untrue. It is a small city and everyone is Newcastle mad.
"When you go out it is not like Manchester or London where you can get lost.
"There are only four or five bars that lads go to so everyone knows where you are going to be. He is a big lad anyway, so he can hardly hide in a corner.
"I hope he manages it, though. There is still a lot of work ahead but Andy has the potential to be a top player."