With only a dwindling band of SPFL Premiership sides in today's quarter-final draw, a hard-earned 2-1 win at Parkhead has left the Pittodrie side - who are already in the League Cup final - favourites to lift the trophy.
Aberdeen reached both major finals under Ebbe Skovdahl in season 1999-2000 only to lose to Rangers in the Scottish Cup and Celtic in the League Cup.
However, defender Mark Reynolds believes the current group of players are made of different stuff to some of the teams of the past.
He said: "I think a lot of people were hoping this week would break our season, but we've come out the other side of it and shown there is a new Aberdeen, an up-and-coming team. The team that was here before would have started crumbling under that kind of pressure."
Celtic have suffered a series of disappointments in the cup competitions under Neil Lennon. They took an lead through Anthony Stokes yesterday but Aberdeen hit back through Russell Anderson and Perter Pawlett.
Lennon felt his side "played like strangers" at points during the match. The Parkhead manager said: "It is in the club's DNA, we're built to win trophies and this was another one I wanted to win.
"We showed [the players] footage of last year's cup final and how much it meant to everyone associated with the club, but it seems to have gone in one ear and out the other.
"Our passing, decision-making, defending, cohesion, partnerships within the team - we played like strangers at times. But we have to give credit to Aberdeen. They played with good energy, were very committed and looked the hungrier team at times. It will take a good side to beat them if they play like that."
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