The Dons take on the high-flying Hoops in the fifth round at Celtic Park on Saturday and Smith, who led the Pittodrie outfit to both the Scottish Cup and League Cup 14 years ago, feels an upset is on the cards.
"It's a wonderful game in prospect at Parkhead. There might have been times when the outcome looked a formality but that's not the case now," Smith told the Daily Record.
"Celtic have been on a fantastic run and an incredible sequence of clean sheets. But that has to come to an end at some point."
Of this year's Dons, who are into the League Cup final, Smith added: "Aberdeen will go there with no pressure.
"They have a cup final to look forward to in March against Inverness and can go to Parkhead almost like they have nothing to lose.
"Aberdeen will go there full of confidence. There is no doubt a psychological barrier has been lifted.
"It's a weight off the club's shoulders because the longer the absence from a final, the harder it became.
"They have a hugely difficult tie at Parkhead but they can win and if they get past Celtic then there's no reason why they can't go on and make it a cup double.
"What an achievement that would be."
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