The three-time world champion was in scrappy form as he fought back to eventually prevail 6-3 over world number 36 O'Donnell in a match that will be quickly forgotten by all.
"There weren't many positives to take from this. I thought it was a poor match from start to finish," said Selby.
"But I won, I'm through to the last 16 and that's the most important thing. I can only improve from here.
"I've been known to win a lot of matches that I don't deserve to win, where I scrap through. So I suppose that helped me in this one. But I don't enjoy playing like that.
Selby will face Matthew Stevens in the last 16, after he defeated Anthony Hamilton 6-2 in the previous round.
Despite Selby's performance against O'Donnell, the Leicester man goes into this one as favourite but he's wary of becoming another victim of an upset in York.
Selby said of Stevens: "He seems to be getting his game back and is a tough player.
"He is a class act, and I think he's underachieved in the game. He's probably not put the work in to achieve what he should, but he seems to be going in the right direction again now.
"I don't think I should be expected just to win this, it doesn't work like that. Look what happened to Judd (Trump) the other day. I just need to focus, play better and try and get through.
"If I do my best that's all I can ask and hopefully will be good enough."
