A new era will begin from 1 July when Everton's Moyes takes over the reins and Carrick is likely to remain a key figure in the new manager's plans.
"As a player, we respect the situation with the manager and he said it himself in his speech at the end about the new manager," stated Carrick to manutd.com. "About everybody getting behind him and supporting him. As players we're looking forward to it.
"It's a change. How much change? We'll have to wait and see but we're relishing the new challenge. With the expectation at this club and the responsibilities you have as a player to keep performing, we've got that drive as individuals and we look to keep the success and go on from year-to-year."