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The nations clash in the last 16 at the Parc des Princes in what is being dubbed as a huge British-style cup-tie.
"We don't want this to end. The players want more," O'Neill said on Friday.
"The prize is massive for both teams. We are playing for a place in the quarter-finals and we have to make sure it is us going through."
Northern Ireland are one place above their opponents in the Fifa rankings, but Wales are the favourites having topped their group ahead of England.
O'Neill's men lost two of their three games and went through as one of the best third-placed teams in the group stage.
"We are happy with that position," added O'Neill.
"Wales are picking a team of Premier League players while we have a mix of Premier League and Championship players.
"I don't think that will play a huge factor. It's an opportunity for our players to show what they're capable of."
O'Neill said his side would be well prepared to try to deal with the threat posed by Real Madrid star Gareth Bale.
"He is a huge player for Wales, but I have had that task before having been up against Cristiano Ronaldo before, and here Robert Lewandowski of Poland.
"We have been extremely strong defensively and played Germany who are full of world class players,
"I don't think we will have a tougher game than we did here on Tuesday night.
"We will be ready to deal with Gareth Bale. We know his threat at set pieces, his running power, pace and goal threat."
O'Neill predicted a highly-charged emotional encounter, adding his players fully understood the significance of Saturday's game.
"Particularly in our last two games, you cannot question the heart of the team from the first minute until the last," the manager added.
"You cannot play without emotion and it will be a big part of the game.
"We came into the tournament with the goal of coming out of our group, which we have managed to do.
"The players deserve an enormous amount of credit for that.
"Now, when you look at the draw, it is easy to get carried away, but we recognise the size of our task on Saturday.
"The players want to be here as long as possible and will do everything they can to do that."
Northern Ireland boss Michael O'Neill says his players are desperate to prolong their Euro 2016 adventure by beating Wales on Saturday.