The Italian is wary of branding their last-16 tie with the Scots over despite holding a 3-0 lead, with memories of AC Milan's collapse in the 2005 Istanbul final still fresh
The 33-year-old was part of the AC Milan team that threw away a 3-0 lead in the second half to the Merseyside club in Istanbul in 2005 and eventually lost the match in a penalty shootout.
The experienced midfielder insists that the bad memory will spur him on in the second-leg encounter, as his current club hold the same advantage against Neil Lennon's side, and he will ensure that his team-mates do not underestimate their opponents.
|17/2||Juventus are 17/2 with BetVictor to beat Celtic 3-0 in their Champions League second leg
"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.
"Celtic, for a start, will be wounded. They are a very proud 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."
Despite their spot in the quarter-finals being all but secure, the former Milan maestro concedes that the Serie A club are not favourites to win the competition.
"We have to be realistic, we know we are not favourites for the Champions League. People will look at Bayern, Real Madrid, Manchester United and, even after their defeat, Barcelona," Pirlo added.
"The most important thing we can do is stay focused against Celtic in Turin — and then we can see what the draw brings after that."
However, his Chilean team-mate, Arturo Vidal, is adamant that the tie is over and that other clubs will be fearful of drawing Juventus in the next stage of the competition.
He declared: "It is impossible for Celtic to beat our score from the first leg. It would take a miracle for them to go through.
"The difference between the two clubs is huge and it is up to us to show in this game we are in contention to win the Champions League. I think this team can go far in the competition."