The Italian champions lead Celtic 3-0 ahead of the Round of 16 second leg in Turin on Wednesday but Pirlo knows football too well to have his hopes pinned on an easy return bout against the Glasgow giants.
Pirlo was a part of the AC Milan side which led 3-0 at half-time before conceding three goals in the second half to eventually lose the 2005 Champions League final to Liverpool on penalties in Istanbul.
"I will never forget the game against Liverpool in Istanbul - for all the wrong reasons," said Pirlo.
"And it is a game I will be reminding myself of before Celtic.
"We are in a very strong position and expect to progress after the result in Glasgow - but we can't think all we need to do is turn up."
He added: "Celtic for a start will be wounded.
"They are a very proud football club and have a very proud set of fans. It will have hurt them to see the way they were beaten at their home - and if we are complacent, then that is when they could have their revenge.
"If we stay professional and concentrate then I am confident we can progress.
"We respect our rivals but to fail against the Scots in Turin would be one of the biggest disasters in the history of this club."