The Red Devils, who face Braga tomorrow night, have collected maximum points from their opening two group matches against Galatasaray and CFR Cluj.
A third victory against Portuguese side Braga tomorrow will go a long way to helping United book their place in the last 16 of the competition.
With that in mind, Carrick believes that United's form in the Premier League would also benefit from a swift progression.
"It does help the league form if you can get through early," Carrick told the Daily Mail.
"The manager can change things around. He can rest players. He can use the squad and give players game time. The pressure is off. He can start planning ahead knowing the next stage is already secure.
"It is not always possible. Sometimes it can go down to the last game, which in itself is not always a bad thing. Overall though, it is better to get it done and dusted."
Carrick was part of the United side that won the tournament on penalties against Chelsea in 2008.