The Black Cats head into today's home clash with Chelsea having won only two of their last 22 league games and stuck one point above the relegation zone.
But O'Neill remains confident there are much better times ahead, and has the experience to back it up. He said: "I've been in management 20 years. I've had tougher times at other clubs and we've come through them.
"When I went to Leicester City, the first 10 or 11 games I couldn't win a match to save my life. We turned that round and were pretty successful.
"The first year at Aston Villa was exceptionally tough indeed. We'll pull round and, inevitably I hope, we'll get a team that the supporters are really proud of.
"It's been a tough start to the season. It hasn't come as any major surprise to me. The team is essentially the same as last season so it's a tough struggle, but we'll get there."
ST Patrick's Athletic are close to completing their squad for the new season after signing Limerick goalkeeper Dave Ryan and Derry City striker Conor Murphy.
Ryan will provide competition to Brendan Clarke for the number one jersey in Richmond Park while Murphy boosts the firepower in Liam Buckley's squad alongside Christy Fagan and Anto Flood.
Meanwhile, Stephen Kenny has continued his rebuild of the Dundalk squad by signing Andy Boyle from Shelbourne.