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 and can have much better campaign this time.
"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.
"Our home form was very disappointing but our away form was good. It's about getting the balance. You want both to be terrific.
"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."