Sir Alex bowed out of English football on Sunday after 1,500 games in charge at the Old Trafford helm. It was some way to finish too after a 5-5 draw with West Brom at The Hawthorns.
Carrick says there was a surreal atmosphere in the dressing room after the manager's final match and maintains that focusing on the future is what everyone needs to concentrate on now.
"We've thanked the manager for everything he's done and he's thanked us," the midfielder told Sky Sports.
"It was a funny time in the dressing room because of the situation.
"It is starting to sink in as we've had a couple of weeks to digest the news.
"We're ready to move on. We've had a busy couple of weeks and there is a new challenge ahead for all of us to look forward to."