The draw for the 2012/13 group stages takes place on Thursday afternoon with the first game scheduled for the 18/19 September.
The Reds were eliminated at the end of last season’s group stages by FC Basel after a disappointing campaign which saw Sir Alex’s men win just two of their six group matches.
Carrick says United are aiming to put things right, particularly at Old Trafford, and while the Barclays Premier League title remains the number one priority, success in Europe is a very close second.
“The league is the priority but when the Champions League comes round, of course, you put everything into it,” the midfielder told ManUtd.com. “We won’t be taking our eye off the ball at all, especially after what happened last season.
"We want to be in the latter stages and fighting for the trophy. But we know the work has to be done now and hopefully we’ve learnt from last season
“The players always look forward to the draw and we’re especially looking forward to it this time after what happened last season. We let ourselves down as a squad."
- Michael Carrick