United will be in Pot One for Thursday's draw, which in theory presents them with an easy passage into the knockout rounds. However, the same was also true last term, with even Sir Alex Ferguson accepting the Red Devils should have advanced, only to crumble in their final match in Basle and crash out of the competition before Christmas.
It is not a fate Carrick expects to be suffering again. He said: "We let ourselves down as a squad last season. 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, Sir Alex 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.
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."