On Tuesday night at Parkhead, as part of the Morton team which will arrive on Scottish Communities League Cup duty, the Slovak hopes to play his part in creating a similar outcome.
The 28-year-old Habai, who has his younger countryman Tomas Peciar for company in the SPFL Championship side's squad, can be forgiven for experiencing mixed emotions in July 2005 as Celtic exited the tournament in ignominy. He was, after all, a boyhood fan, was playing at the time for Artmedia's city rivals Slovan, and it was in their Tehelne Pole stadium that the match actually took place.
But, with Celtic's 4-0 victory in the return leg at Parkhead a week later unable to overturn the aggregate, the overall importance of the result to Slovakian football took precedence. And while the Artmedia dream turned sour soon afterwards as mega-rich sponsor Ivan Kmotrik withdrew funding, Habai also subsequently played there for a season as the club, now known as FC Petrzalka, attempted to rebuild in the lower divisions.
"I was there at the stadium when Artmedia Bratislava beat Celtic, but as a fan, not as a player," said Habai. "If Celtic were playing against Slovan Bratislava, then I would definitely have wanted Slovan to win. I was at Slovan for 10 years in total, three years as a professional, and they are my team. When Petrzalka and Slovan were both in the first league together, at every game they were big rivals, a big fight. So maybe I was neutral…
"But, no, this was a very important match for Slovakian football so for me it was probably more important for the Slovak team to beat Celtic," added the player, who can play in defence or midfield. "I think Artmedia were a bit lucky to go into the Champions League that year, though, because if the return match had lasted 10 minutes longer Celtic would have won."
Had things gone differently in another sense, Habai could have been playing for Rangers right now rather than Morton. He and Peciar ultimately arrived in Greenock courtesy of manager Allan Moore's connection with an agent, John Joseph Petric, who had previously helped bring cult hero Marek Tomana to Stirling Albion. Cue a whistlestop tour of Slovakia for Moore, and the two chosen targets playing a number of matches as trialists. But that was only part of the story.
"When I first came here, I played in a friendly against Sheffield United," said Habai. "Lee McCulloch, the captain of Rangers, was watching and two days later they called our agent and wanted me to go for a trial at Rangers. But I said, 'no, I am going to stay here'. I wasn't tempted to ask more about Rangers because we had been here for two weeks before Rangers asked if they wanted me to go there. It wasn't 100%, but I knew it was 100% here."
The Slovakians - both of whom have played for their country at youth level - are likely to play on Tuesday night, not least because veteran defender Mark McLaughlin suffered a facial injury against Livingston last Saturday. Even if Celtic, as suspected, field a weakened team and the crowd is down from its usual levels, the tie promises to be a personal highlight for the two Slovaks.
"We have been to Celtic Park before, when Celtic played Elfsborg in the Champions League qualifiers," said Peciar. "We could tell that night that Georgios Samaras is a very good player, he is very dangerous either in left midfield or as a striker, but I hope he won't play against us.
"They played in midweek in Milan, then in the league on Saturday, then they have Barcelona at home a week on Tuesday, so hopefully four or five first-team players won't play and I hope Samaras will be one of them."
Celtic, of course, have a strong Slovak connection themselves in the form of Stan Varga - another veteran of that 2005 Artmedia matchday squad - and a certain Lubo Moravcik. "Even years ago we used to watch Celtic on Slovakian TV," Peciar said. "Celtic had Lubo Moravcik and Stan Varga, two Slovakian players, so there is a connection and we watched every time ... even though Lubo is probably a bigger hero here than in Slovakia."