Northern Ireland have been one of the surprise packages of the tournament, reaching the knockout phase after beating Ukraine and losing to world champions Germany and Poland by just a single goal.
They go into the game at the Parc des Princes having last beaten Wales in 1980, although the two sides played out a 1-1 draw in March.
"The words of wisdom for the team are simple: find the game of your life tomorrow night. The game will have a bit of a cup-tie feel to it," O'Neill told reporters on Friday.
"We recognise the size of the task tomorrow night. I expect Wales are the favourites, but we played here three nights ago against the world champions and we won't get a tougher game in the tournament."
O'Neill's team has been built on a solid defensive unit which is happy to give possession to the opposition in the hope of breaking quickly when the opportunity arises.
They topped their qualifying group for the tournament with 16 goals from 10 games despite seeing less of the ball than all the other teams except for the Faroe Islands.
"It's what we do with the possession," O'Neill said. "The main thing is how we defend as a team. That has been our strength and we've gained confidence from that."
While lauding Welsh forward Gareth Bale's great qualities, O'Neill said his team had no reason to fear him having faced players of a similar stature.
"It's up to us to ensure that Gareth Bale has a quiet night," he said.
The game will be officiated by English referee Martin Atkinson, giving the fixture a real British feel.
"The main thing is that we make the game a cup tie. We have an English referee and we want everything that is good about the British game to come out," O'Neill said.
"We want to play the game in the right way and do our best. We expect a good-old fashioned British game tomorrow night."
(Reporting by John Irish, editing by Ed Osmond)
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