Goals from Alejandro Dominguez and Arsenal loanee Joel Campbell saw the Greek hosts claim a 2-0 first-leg lead over the reigning Premier League champions to compound a miserable season for the Red Devils.
But Carrick, who still insists the side can progress to the Champions League quarter-finals, believes the onus should be on the players to step up and rejected suggestions they were missing Sir Alex Ferguson's presence.
|MAN UNITED LATEST
|40/1||Manchester United are 40/1 with Paddy Power to win the Champions League|
Carrick also offered a bullish response to United's detractors, and, after being heavily criticised in the wake of the Olympiakos result, is keen to silence the club's many doubters.
“We've set standards as players over the years and this season hasn't gone so well,” the midfielder continued.
“We're there to be shot at and we're getting criticism from all angles, everyone is having a bit of a dig and enjoying it, so we've got to take that on the chin and bounce back. I'm sure we will.”
Despite needing to overturn a two-goal deficit, Carrick is hoping to use previous European comebacks to inspire a revival and get the three goals United will need to progress.
“It would have been nice for us to get an away goal near the end but the tie isn't over yet, we thoroughly believe that, but it's not ideal,” he added.
“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.”