The 74-year-old hailed the Lisbon Lions - who delivered the club's greatest ever achievement when they lifted the European Cup in 1967 - for "setting the bar" and wants his side to replicate their success despite the financial challenges of modern football.
The Celtic manager also expressed his "disappointment" over losing influential midfielder Arne Engels to West Ham United just days before Wednesday's crucial £40m showdown.
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After being knocked out of Europe's premier competition at this stage by Kazakh side Kairat Almaty last year, the champions of Scotland return with fresh faces and a point to prove.
O'Neill: We should be aiming to win the Champions League
When the Estadio Metropolitano stages the 2027 final in Madrid next June, 60 years will have passed since legendary captain Billy McNeil got his hands on the trophy - the iconic image of which is cast in bronze outside Celtic Park.
Football has changed in the intervening six decades with Scottish sides no longer able to compete with the financial might of elite clubs in England, Spain, Germany, France or Italy.
However, O'Neill - who won the European Cup twice as a player with Nottingham Forest - has set his players the improbable task of emulating the club's most famous heroes:
"I've said all along, I think that the bar was set down here way back in 1967," he said at his pre-match news conference.
"From then on, I believe that Celtic should be aspiring to that. We may never, ever, ever get there and obviously with the way that the financial market has moved in football, it's getting more and more difficult for maybe a team from Scotland.
"But that aside, you should still be aspiring to it and that's what we want to try and do. We may never get there but this is the bar that's been set down, and the football club have won the European Cup or the Champions League, whatever it's called.
"Really, that's what we should be trying to do, and we'll make an all-out effort to try and make it."
How much is Champions League qualification worth?
While prestige and platform may motivate players and managers, money keeps boardrooms happy.
Celtic banked more than £40m from their last participation in the Champions League in 2024/25, where they were beaten by Bayern Munich in the first knockout round.
If O'Neill's side are able to successfully navigate their play-off with LASK this year, they will receive around £16m in automatic prize money - even if they lose all eight league phase matches.
Thereafter, every draw in the competition is worth £600k and every win is worth £1.8m. There are also financial rewards for every place in the final league phase table as well as for every round of the knockout stages.
In addition, according to Football Meets Data, Celtic are due to receive between £14.4m and £16.6m from Uefa's complicated 'value pillar' financial distribution model - which ranks participating clubs based on coefficient points and TV market ratings. Therefore, the final figure could change depending on which teams progress to the league phase.
Furthermore, based on previous gate receipts and ticket prices, four sold out home Champions League fixtures at Celtic Park could yield a further £10m in gross ticket sales.
Thus, before kicking a ball, Champions League qualification could be worth an estimated £40m.
Killing the Kairat derailer
Twelve months ago, a fifth consecutive exit in Champions League qualifying threatened to derail Celtic's season.
The result, paired with a perceived lack of activity in the transfer window, prompted a series of fan protests aimed at the club's board which punctuated a tumultuous campaign at Celtic Park.
The hierarchy were accused of 'neglecting' the team, 'sleeping at the wheel', and 'gambling' Champions League qualification via official supporters' group statements and ultras' group banners.
However, this summer, the club have reinvested significant funds in the playing squad; more than £30m has been spent on the acquisitions of Kasper Hogh, Camilo Duran, Hasseim Hassan and Mika Baur.
And despite losing key contributors such as Engels, Daizen Maeda, Kasper Schmeichel, Kelechi Iheanacho and Marcelo Saracchi, manager O'Neill feels his side are well-equipped to deal with LASK:
"I think that the players who are still here at the football club, they may well remember it, they may well think that they've got something to try and achieve this time," he added.
"But overall, I think we're just trying to look forward to the games, trying to get a result in the matches and trying to get through.
"I like the players that we've signed. I think I said last weekend that ideally it would be nice if, for instance, [Hasseim] Hassan had a little bit more football played.
"That's the nature of the game. We've got him in now and over the course of the season, whether it's in the Champions League or whether it's in the Europa League, it's up to the players now as much as anything else.
"I think the quality that we've brought in will bear fruit during the course of the season."
O'Neill: Can't replace Engels before qualifiers
The loss of Engels may have felt inevitable, but the timing is far from ideal.
The Belgium international was subject of a £25m bid from Premier League side Nottingham Forest on deadline day in January before eventually leaving for £22m to West Ham United this summer.
However, the midfielder's departure was not confirmed until Saturday, leaving O'Neill with insufficient time to recruit a direct replacement.
The manager has a wealth of central midfield options - including new signing Baur from Paderborn - but lacks a like-for-like match of Engels' physical profile.
"Arne [Engels] wanted to go, he didn't want to play in the matches in case he got injured," continued O'Neill.
"I said again last week that was understandable if this is a move that he wanted to make.
"But for the football club, yes, it's disappointing because just at this moment, he's hard to replace in the side with that sort of running power that he has and that he gives us.
"So just even for these two games, that's disappointing, but it is what it is and there's nothing we can do about it.
"We're still in the process of trying to do that [find a replacement] and we haven't been able to get someone in time. There are a number of players that we are looking at and hopefully we will by the end of the transfer window."
