The Manchester United midfielder was forthright in his post-match interview, blasting his side's performance.
Louis van Gaal's side threw away a one-goal lead to lose 2-1 in the first leg of the last-32 clash and suffer one of the most ignominious defeats of their season.
A shellshocked-looking Carrick struggled to find the words to explain the shock result, and accepted that the performance was unacceptable.
The 34-year-old said: "It's just not good enough. It's not acceptable, it's got to be a lot better.
"I think we caused a lot of our own problems, but all in all it's just not good enough, we haven't played well enough. We didn't really kick on after we scored.
"It was there for us to win the game and we should have won it, but with a performance and a result like that we're going home very disappointed."
The loss was a tenth defeat of the season in all competitions for Van Gaal's side, and is likely to significantly increase the pressure on the Dutch manager regardless of whether United ultimately progress.
Being knocked out of Europe would be a blow for the Red Devils, who are struggling to breal into the top four and sit six points off a Champions League spot in fifth.