Despite Sir Alex Ferguson's side making their worst start to the season for six years, Carrick remains convinced they can overhaul the Londoners.
That attitude, he says, is born out of Ferguson's insatiable appetite for success - revealing that he was made aware early on in his United career that second best will never be good enough.
"It's unbelievable here," he told the Manchester Evening News. "No disrespect to the teams I played for in the past, but we'd go away and a draw would be a good result. You don't get that here.
"You've got to go and win. Believing you can win anywhere was a feeling I'd never had before.
"I remember my first start was in a 2-1 win at Watford and after the game the manager gave the team a right going over.
"I wasn't used to that. I was buzzing after a win. I learned there's a way of doing things at this club. I became accustomed to it.
"To come to a team like this is incredible. It is the stuff of my dreams. Not just playing with them, but training with them and seeing how they live their lives.
"That attitude all comes down from the manager and it certainly rubs off on every player who walks through these doors.
"It's a daunting thing to do at first. Before I came I spoke to Rio Ferdinand about it, he was the same on his first day of training - and he was a proven international.
"Nothing prepares you for walking through these doors. You've got to justify being here and show you're worth it - but you quickly fall into the routine."