The 32-year-old could face direct competition for his first-team spot from the versatile Belgium international, but he believes the challenge will only serve to help him improve.
United signed Fellaini for £27.5million on deadline day, seeing the 25-year-old link up again with former Everton manager David Moyes.
Carrick started in 34 of United's 38 Premier League games last season as 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.
And the England international has welcomed Fellaini's arrival as well announced an intention to carry on playing for as long as possible.
"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," he said.
"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.
"I can't deny last season probably was my best one.
"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."
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