Fellaini impressed during his first ever game in the competition as the Reds secured a 4-2 victory in their opening Group A match.
Carrick says the Belgium international has fitted in well and that his arrival has afforded David Moyes another excellent option in the squad.
"It was good to play with him. He’s a real presence in there," Carrick told MUTV. "You could see tonight that he’s such a dominant player and he gives us something that we haven’t had and that’s exactly what you want – options in the squad.
"Sometimes you want to play different ways and he gives us that option. There’s no point in having similar players. He’s fitted in well and settled in great. He’s a top player and we want as many of those that we can get."
Tuesday's win, on the back of three points in the league against Crystal Palace at the weekend, is exactly the boost the Reds wanted ahead of Sunday's trip to Manchester City.
"Tonight gives us a lot of confidence going into Sunday. As a package it was a polished all-round performance," added the England international.
"We’ve had a stop-start beginning to the season and people have been asking questions as normal. Tonight we got a good performance and result. We really meant business, we knew how important it was to get the result and thankfully we did that."