But they lost momentum and had to be content with sixth spot.
O'Neill, whose side currently lie in fourth spot, said: "Last season we were still going very strong in February time but lost a couple of matches in relatively quick succession.
"We lost to Chelsea, drew with Stoke and lost to Manchester City and we were rocked, knocked back and lost a bit of confidence.
"While we regained it eventually by finishing in the top six and getting into Europe - which I think is sometimes forgotten - we were unable to sustain the run.
"The same thing might happen again. We are on a decent run but the Premier League is very unforgiving.
"You are going along nicely, you win a couple of games but then you pick up a couple of injuries, lose a game and want to know where the next win is coming from.
"I think it's very much the case of same again. We are hanging in but we're playing well, with plenty of confidence. We are managing to win games when we go behind and when we get in front too.
"But I heard Harry Redknapp speaking the other day about how fickle it all can be.
"He said you can win two consecutive games and you're unbeatable and you lose a couple of games and you're useless. I think the same applies to us."
O'Neill, whose side visit Arsenal on Sunday, added: "We have some really talented players performing at the top of their game at the moment. I just would like that to continue.
"But there are so many things that can knock you. I mentioned the injuries but there are also suspensions and obviously the opposition is strong.
"Look at last week's midweek results. The top sides are still finding it difficult to win convincingly but they are still winning.
"It's hard hanging in there but the players are finding it exciting."
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