Having taken over from Steve Bruce with Sunderland in a similar position 12 months ago, O'Neill made an instant impact and appeared to have turned things around, but the end of the campaign was tough and they have carried on in the same vein this season.
The Black Cats head into Saturday'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 he 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."
As well as his own experience, O'Neill also believes last season's struggles put Sunderland in a good position to turn things around.
He said: "There's lots of elements attached to this. The unity is very important of course but the players this time last year were in a similar position so we've got a bit of experience of that.
"We'd obviously hope that experience plus the spirit that exists in the squad would give us a headstart."
The club's fans have so far stuck by O'Neill but the frustration has been evident in recent weeks and, with Saturday's game followed by another home match against Reading on Tuesday, it is an important week for the club.
"I think all clubs hope their fans stay with them but of course there's a frustration at this minute," said O'Neill.
"That frustration has been borne out of a long time where the club has underachieved for its size, and I don't just mean over the last couple of years, I mean for a long time.
"That frustration is there but by and large the crowd are willing the team to do something so they can support them. It works both ways. We've got to do something to enthral them."
Last weekend brought another defeat, 2-1 at Norwich, but there were at least encouraging signs in the second half, and Sunderland really should have got at least a point.
Chelsea arrive in the north east also in need of a win after seven league matches without one - a run that has seen them drop 10 points behind table-toppers Manchester United.
Rafael Benitez at least managed a first win as manager in the Champions League on Wednesday, 6-1 over FC Nordsjaelland, but it did not stop the holders going out of the competition.
O'Neill said: "I was watching them on Wednesday evening and, despite the fact they went out of the Champions League, they're a very fine side. They've got a lot of attacking options, they spent heavily in the summer to try to improve their team.
"They'll be disappointed they didn't qualify for the knockout stages but the fact their next couple of games are in the World Club Championship might tell you how far they've come."
The Sunderland boss may be able to select defender John O'Shea and striker Steven Fletcher on Saturday.
O'Shea has begun to train again after a calf injury while Fletcher saw a specialist about the ankle problem that forced him off at half-time last weekend but has not been ruled out.