United will be in Pot One, which in theory presents them with an easy passage into the knockout rounds - Manchester City, Chelsea, Arsenal and Celtic will also be in Thursday afternoon's draw.
However, United were in a similar situation last season. Even Sir Alex Ferguson accepted the Red Devils should have advanced, only to crumble in their final match in Basel and crash out of the competition before Christmas.
It is not a fate Carrick expects to be suffering again.
"We let ourselves down as a squad last season," said Carrick. "We won't be taking our eye off the ball at all.
"We want to be in the latter stages and fighting for the trophy. But we know the work has to be done now. Hopefully we've learnt from last season and can have much better campaign."
Purely on geographical grounds, Ferguson will be looking to avoid the likes of Zenit St Petersburg, Shakhtar Donetsk and BATE Borisov.
However, Juventus and cash-rich Paris St Germain are very dangerous opponents from Pot Three and Ferguson will be just as keen to sidestep them as well.
At least Jonny Evans' reserve-team run-out against Tottenham on Wednesday night following his summer ankle operation suggests the Red Devils will have additional defensive strength when their European campaign begins next month.
Darren Fletcher also continued his hoped-for comeback from his chronic bowel condition, whilst new-boy Alexander Buttner started his first United match since arriving from Vitesse Arnhem last week.
It should help Ferguson ease United through, no matter who they get, although Carrick believes their results at Old Trafford hold the key.
"Our home form was very disappointing last season," he said.
"You need your home form to be terrific to give you the base to progress.
"Over the years it's been good and we'll be looking to put that right this time because we don't want what happened last year to happen again."