Carrick is still confident that the Red Devils will advance from the return leg next week, but the England midfielder pulled no punches when asked about his side's performance on the night.
"It just is not good enough. It is not acceptable. It is nowhere near good enough. It has to be a lot better," Carrick told BT Sport.
"We caused a lot of our own problems. We just have not played well enough. We should have won the game, but we will go home very disappointed.
"We have another chance to put it right. It will not be easy, but playing at home we will fancy our chances. We have given ourselves a tougher job than we would have hoped."
Man United lost number one goalkeeper David de Gea to an injury during the warm-up in Denmark.