Julian Schieber scored the winner after 57 minutes to consign Mancini's side to the bottom of the group, having failed to win any of their six games.
"I don't think we lost our qualification tonight. We lost before tonight," said Mancini.
"We had the chance to score but if in these moments you don't score it's difficult to win.
"We are not in the Europa League, and for this we should be disappointed.
"I think last season we did better but this year we had a very difficult group. If you make a mistake in the first two to three games it is difficult to recover.
"Clearly this can help us in the Premier League because we won't be playing in the Europa League but we wanted to. That was our target tonight."