The Hoops face LASK at Celtic Park in the first leg of their crucial play-off on Wednesday, with a place in the league phase at stake.
Celtic have until 11pm on Tuesday to register any additional players for the tie, but O'Neill has played down the prospect of a late arrival.
Speaking to the media ahead of the game, the Celtic boss was asked whether he expected any more players through the door before the deadline.
O'Neill replied: "What time is the final thing?
"Is it 11? Well, that, I really wouldn't be sure.
"A fairly decent chance of nothing happening."
Celtic have already made four major additions this summer, all of whom will be available against LASK.
Asked whether he is comfortable with the squad at his disposal, O'Neill continued: "Well, I like the players that we've signed.
"I think I said last weekend that ideally it would be nice if 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 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."
One significant player Celtic will be without is Arne Engels , whose £22million move to West Ham United has been completed since O'Neill last addressed the media.
The timing leaves Celtic without one of their key midfielders immediately before two of their biggest matches of the season, and O'Neill conceded that losing Engels at this stage was a blow.
Asked whether the timing of the sale was a disappointment, he said: "Of course it is, yeah.
"I think Arne wanted to go. He didn't want to play in the matches in case he got injured. I think I said again last week, that was understandable.
"This was a move that he wanted to make, but for the football club at this moment, it's hard to replace in the side, that sort of running power that he has, and that he gives us.
"So just for these two games, that's disappointing. It is what it is, and there's nothing we can do about it."
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