City were dumped out of the competition by Aston Villa.
"It was a difficult match because Aston Villa were a good team," said Mancini.
"We didn't play well and we had some unlucky moments but I think they deserved to go through.
"We are so disappointed. We didn't play well and our play is not quick, we want one touch more every time and this is no good.
"It is the fourth competition but it is the only competition we didn't win and for that reason we wanted to stay in this cup because in two years we have won everything and are missing this one."