The Scotsman bowed out as Red Devils boss with a thrilling 5-5 draw with West Bromwich Albion on Sunday and his unprecedented success in the game was certainly not lost on midfielder Carrick who enjoyed his best season in helping the club clinch their 20th title in 2012/13.
"I want to thank him for everything he's done, he's done much more than us," Carrick told Sky Sports.
"It was a funny time in the dressing room because of the situation.
"It is starting to sink in and 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."