Carrick scored two goals in last night’s 7-1 triumph over Roma.
He told MUTV: “We’ve got the belief, we’ve certainly got the quality, the desire and everything that goes with it.
“The confidence we have in each other has grown throughout the season. We’ve had setbacks along the way but we’ve always come back even stronger and I think tonight was a classic example of that.”
“When you’re at this stage, you need little things to go your way. If we have that little bit of luck, then we can do it. We’ve got as good a chance as anyone else now.
“At this stage every team has got an awful lot of quality and it’s a big test. We’ll be watching and enjoying the game tomorrow (between AC Milan and Bayern Munich).
“It was an incredible night, a really special occasion. There was a big build-up to the game and for it to go like that it was unbelievable. It’s a night that I won’t forget for a long while.
“The first goal was obviously crucial, it gave us a great chance of winning the tie. But to get seven… well, you can’t believe that.
“Sometimes you get one, two, maybe three goals and then take your foot off the pedal, allowing the other team to come at you. But we didn’t get sloppy at all tonight, we kept going and our forwards were unbelievable, causing so many problems.”