The 32-year-old could face direct competition for his first-team spot from the versatile Belgium international, who was reunited with former boss David Moyes on deadline day, but believes that the challenge will only serve to help him improve.
"The more top-quality players you have in your squad, whether it's in my position or not, the better it is for the team," Carrick told the press.
"It's not a case of me thinking I might not be in the team, I will still have to play well to be in it regardless."
Carrick started in 34 of United's 38 Premier League games last season as Sir Alex Ferguson guided the club to the title before retiring in what the former West Ham and Tottenham man dubbed the "best" campaign of his career.
But the England international refuses to see Fellaini's arrival as any sort of indication that his time in the first team might be coming towards its end.
"I can't deny last season probably was my best one," he added. "There's no reason why I would be thinking of packing up any time soon.
"You never know what's around the corner but I wouldn't say it was going to be my last one."