The Red Devils hardly fired a shot against the Greek SuperLeague champions in Piraeus in what was another unsatisfactory result for David Moyes' men.
"It's a disappointing night," Carrick said. "To lose like we have is hugely disappointing.
"I feel we still have a chance going back to Old Trafford but obviously it's not going to be easy.
"We've lost the game and we can here hoping to win but we haven't done that. We are not out of the tie by all means but it's not ideal."
The return leg takes place in Manchester at March 19 and Carrick is already targeting a much-improved showing back at the Theatre of Dreams.
"As players we haven't been getting good results and as a club that's everyone involved. That's how we are judged and we know that," he added.
"We're still in the tie, we're going home, we're not out of it at all, so we look forward to the second leg."
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