Having lost 1-0 to Poland in a tame opening performance, and with world champions Germany still to come, O'Neill's team need to beat Ukraine to have any real chance of making it through to the last 16.
"What we didn't do well the other night was the ugly part of the game, and that's something that we generally always do well. So we have to make sure that we bring the ugly side of the game tomorrow night," O'Neill told a news conference.
"And when I say ugly, I don't mean 'out with the rules', of course, I mean just in terms of the level of competitiveness, because I think what we have seen is that every game of the tournament to date has been extremely competitive."
O'Neill turned the tables on a journalist who referred him to comments from Ukraine midfielder Ruslan Rotan that Northern Ireland played 'purely a British style, with great physical preparation, strong flanks, high crosses and lots of scrambling.'
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O'Neill said the Ukrainians themselves had played that way in their opening loss to Germany, with a lot of long balls and not much possession.
"I think if you look at the yellow and red cards the Ukrainians have had this season, and through qualification, you'll see that obviously I don't think they're playing a Spanish style of football.
"So we expect a tough game physically, but we expect a highly technical game as well."
For much of the Poland game, striker Kyle Lafferty cut a forlorn figure on his own up front for Northern Ireland, although Conor Washington came on as substitute to join him in attack.
O'Neill would not be drawn on whether he would start with one or both against the Ukrainians.
"There's not many teams in the tournament will play with two out-and-out strikers if I'm honest, so we have to just think about whether we start with that or whether we introduce it as the game progresses."
Asked whether his team, at its first major championship in 30 years, had been buoyed by the strong showings of underdogs Iceland and Hungary, O'Neill said: "I don't think we needed that reassurance, like, 'Do we belong here?'
"We've felt that all along, but obviously we have to demonstrate that tomorrow night against a strong Ukraine team.
"We want make sure tomorrow night that the game, we play it like a cup final."
(Reporting by Mark Trevelyan; Editing by Ian Chadband)
