Instead, the midfield maestro emerged with a Treble – and a place in Celtic folklore.
Now Moravcik can see the same opportunity opening up for the current crop of Hoops players.
And the Slovakian superstar believes the mentoring enjoyed by former team-mate, Neil Lennon, when he was a key figure in O'Neill's side, is one of the reasons the rookie boss has turned the club around.
O'Neill performed a similar U-turn after assuming command from John Barnes and Kenny Dalglish in the summer of 2000.
Celtic had finished the previous season 21 points behind Dick Advocaat's team.
But, soon after lifting the League Cup with a 3-0 victory over Kilmarnock on March 18, 2001, O'Neill's side clinched the SPL championship with a 1-0 win over St Mirren at Celtic Park before completing the Treble with a Scottish Cup Final win over Hibs on May 26.
Moravcik, who had been brought to the club from Duisburg two years earlier by Dr Jo Venglos, savoured every minute – not least because he reckoned his time at the club might have been up when O'Neill arrived and initially failed to appreciate the qualities he could bring to the side he was building.
Lubo explained: "Martin's first season at the club carries so many good memories for me, but it did not look like it was going to go the way it did for me.
"When he took over, we had had problems, as you could see by the way the championship had finished the season before. But the way things turned around so quickly, I immediately knew Martin was the right man to put Celtic back on top.
"Unfortunately, at first, I had a bit of problem because the way he was going to do this did not appear to include me.
"Unlike Dr Venglos, who had been my international manager and had brought me to Celtic Park, Martin did not know me at all."
He added: "To begin with, he did not know what I was capable of doing for the team. But after a small conversation, it all changed, and I had the best season of my career.
"Martin is an intelligent man, and it was possible to sit down and talk with him. I asked him his opinion of me, and he admitted, 'I don't really know you'.
"I told him, 'I can offer your team this,', and added that if it was not of any use to him, then maybe I could find myself another club."
To the relief not only of Moravcik, but everyone at the club and their adoring supporters, O'Neill decided to take the veteran at his word and gave him his chance to deliver what he claimed he could bring to the party.
Within months, O'Neill had reason to be grateful he had taken this decision as Moravcik quickly became a key figure in a side which also boasted the likes of Henrik Larsson, Chris Sutton, Lennon, Paul Lambert, Didier Agathe and Johan Mjallby.
O'Neill spent big bucks to bring to the club the quality he knew it would take to undo the damage done through years of under- investment.
But there were already important players in situ, including Moravcik, who had cost a bargain £30,000 in November 1998.
What was required was the right man to pull them all together and set them on a course to becoming the dominant force once again in Scotland, and re-establishing their name as a credible force in Europe.
Moravcik is now watching O'Neill perform a similar Lazarus act with Sunderland, and said: "It was an amazing turnaround in just one season at Celtic. But if you look at what he has been able to do at Sunderland, you understand what an important guy he is. Everything that happened at Celtic at that time happened because of Martin.
"We had a very good team under Dr Venglos, and we came close to winning trophies. And, even the season John Barnes and Kenny Dalglish were in charge, we won the League Cup.
"We had Henrik Larsson, Paul Lambert, Johan Mjallby, guys like that. We just needed the right manager.
"Martin gave us the confidence to play to our best, and, of course, he also brought in a number of other very good players."
Nevertheless, the rate of turnaround, and the fact they lifted the Treble in the first season of O'Neill's reign, caught even the experienced Moravcik by surprise.
"We knew it was special to win a Treble," recalled Lubo. "The fact only Jock Stein had managed it before in the club's entire history told us that.
"It was the third time Celtic had taken all three trophies, and this year I hope it will be the fourth.
"Neil Lennon had a very good teacher in Martin, and I really hope he can go on to become only the third Celtic manager to lead the club to a Treble."
It may have taken Lennon two years to get to the history-making point which O'Neill reached inside his first season as Celtic manager, but the symmetry between the two is still there for all to see and appreciate. Moravcik will be cheering the 2012 Celts all the way to what he hopes will be the winning line this season, and, like Lennon, he reckons that for this group it should only be the beginning.
"I have followed the progress the team has made since he took over two years ago, and I believe he has built a very good team with a lot of young players," said Lubo.
"I hope they can go and take the Treble because such opportunities don't come around very often and Neil deserves it for the work he has done."