Speaking ahead of Thursday night's Premier League fixture against Arsenal, the temporary boss also paid tribute to the club's backroom staff.
Carrick stepped up from his role as first-team coach after the departure of Ole Gunnar Solskjaer less than a fortnight ago. The former midfielder has overseen an important victory in Spain against Villarreal and a draw against league leaders Chelsea at Stamford Bridge on Sunday.
With Ralf Rangnick confirmed as United's new interim manager, Carrick is to step back into his old role soon, but remains in charge for Thursday's game as Rangnick waits to complete the work visa process.