Pirlo was released on a free transfer to join Juventus, but so far no midfielder has been brought in to replace him.
"There was an alternative, but we were unable to complete the transfer. We had identified a few targets, though some did not make the move.
"In any case, there are still a few days left in the transfer market, so last year at this time we brought in Zlatan Ibrahimovic and Robinho. It's possible someone else can be a late arrival too," said Allegri.