Despite the club's 2-0 defeat to Olympiakos on Tuesday evening, the midfielder claims the Premier League champions can secure a turnaround in the second leg at Old Trafford
David Moyes' side face a tough task of progressing in Europe after goals from Alejandro Dominguez and Joel Campbell handed the Greek champions victory on Tuesday evening.
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"It's a disappointing night," Carrick told ITV. "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."
United managed to register only one shot on target in their defeat to the Greek side, and Carrick admits his team-mates must take responsibility for their sub-par performances this term.
"We haven't been getting the right results," said the midfielder.
"As players we've got to stand up and take it on the chin. You take the good times and the bad times.
"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.
"We're still in the tie, we’'e going home, we're not out of it at all, so we look forward to the second leg."