The Reds produced a below-par display in Athens and face an uphill task to reach the last eight after goals by Alejandro Dominguez and Joel Campbell for the Greek champions.
Carrick admitted United weren’t good enough but believes David Moyes’ men can mount a fightback in the second leg in three weeks’ time.
"It's a disappointing night," Carrick said. "We came here hoping to win and we haven't done that. We didn't react in the second half until it was too late.
"We had good possession in the first half, controlling the game without really penetrating through their lines and causing them any problems. They didn't really cause us any problems and [Dominguez’s] goal came from nothing.
"We didn't start the second half very well: we were a bit sloppy really and they scored the second goal, which put us on the back foot.
"But we're not out of the tie. We are still in with a chance going back to Old Trafford and we'll look forward to the second leg. Don't get me wrong: to score three goals in this competition is tough, but we've done it before and we believe we can do it again."
Robin van Persie spurned a great chance to bag an important away goal in the final 10 minutes but Carrick refused to point the finger at the striker and says the whole team must shoulder responsibility for this season’s disappointments.