The Hoops have won 13 out of the past 14 Premiership titles and numerous other trophies in recent years, but the current campaign has been chaotic.
Northern Irishman O'Neill is in his second spell as interim boss this season after being manager of Celtic between 2000 and 2005, and finds himself embroiled in a tight title race.
Celtic are five points behind leaders Hearts and one point ahead of Rangers going into Sunday's Scottish Cup quarter-final tie against their fierce Glasgow rivals at Ibrox.
"The overall picture is I think that it should be a wake-up call for the football club," said the 74-year-old O'Neill.
"You could say that in recent years, fans have maybe been spoiled, with no real challenges in many aspects.
"Being able to coast home in the last six or seven games of a season, which is great because you've done that. But the challenge has not been strong."
O'Neill said Hearts had "arrived on the spot" earlier than had been expected, and Rangers had also improved.
"So it's been a challenge all season and certainly been the challenge in my couple of spells in here, where you're winning some matches, and you're still trying to peg teams back," he said.
"But we're in with a chance anyway, that's the point.
"I don't think it (Sunday's game) would have a serious bearing (on the Premiership title race) but in terms of confidence-building, of course, those things always matter."