United crashed out of the Champions League after a shock 2-1 defeat to Basel in Switzerland.
"It feels like a dream," Evra said.
"I feel I will wake up tomorrow and we will have qualified.
"But it is not a dream it is the reality. We should have woken up earlier in this competition. We deserve to be out.
"Even if it is a friendly, when I pull on United shirt I do my best to win that trophy. But it is embarrassing to be in the Europa League.
"I play for Manchester United to play in the Champions League but some players dream of playing for United in any competition and you have to respect that."