Carrick has come under harsh scrutiny, but Fletcher believes the England international is responding in the perfect manner.
Fletcher said: "Michael has answered the questions where it matters, on the pitch.
"He was fantastic at Swansea and again against Benfica, arguably man of the match.
"He's such an intelligent player that he maybe does things that go unnoticed, but the players, manager and staff at the club are fully aware of how good a job he does.
"He's great to play alongside. I think we have an instinctive understanding. We always know what each other is doing and where we're going.
"I think we complement one another.
"But the manager has got so many options in there. Different games call for different partnerships, so it's up to us whenever we go out there to show that we deserve to be in the team."