Bilic, who is Croatia’s national coach, described England as “s***” in the Sun last week.
Carrick said: “Whatever comments he wants to make are up to him — but we don’t have anything to prove to him.
“People are always going to have some kind of opinion and differing views on the England team but we can’t let any comments affect us.
“We’ve got to win on Wednesday night, no matter what anyone says.
“England coming to town is a big game for Croatia and they’ll want to do well. But we’ve got our own agenda and that is simply to win the match.”
He added: “The measure of the team is how we respond to the first disappointment under the new manager.
“There is no denying that Saturday was a huge let-down for all of us and a very frustrating day. We had opportunities to score but we didn’t take them and now we’ve got to get that result out of our system as quickly as possible.
“It’s a bit of a stumble but our confidence and belief haven’t been knocked. The attitude and ability are still there. We all know we’re better than we’ve shown at the weekend but there is no point dwelling on a result we can’t change.
“We’ve got to look forward and bounce back straight away against Croatia.”