Now a similar challenge is confronting the Reds, who visit fourth-placed Villa on Tuesday night, after a below-par opening half of the season and O'Neill believes they are capable of the same sort of feat.
O'Neill, whose side won 3-1 at Anfield in August, said: "Liverpool have lost a few games more than they would have thought. Last season they were terrific.
"They went through the whole season and lost two games. After three games of this season, they had lost two games, but they are getting a bit of momentum again.
"It was a big win for them at Anfield against Wolves at the weekend. We've got to be right ourselves, but they are still in there.
"I heard Arsenal were supposed to be imploding last season, just about February time, when I think they were in the middle of a 22-game unbeaten run!
"They finished the season very, very strongly and Liverpool are capable of doing the same thing. They are capable because it's Liverpool Football Club.
"Look at Arsenal now. Four weeks ago they were being written off for the title and now they are right bang in there. That's what can happen with the top clubs."
O'Neill is unconcerned at what reaction there will be to Villa's 3-0 defeat against Arsene Wenger's side and does not believe his players will suffer any hangover to that setback for when they tackle Liverpool.
He said: "I'm not too bothered about who says what. I didn't get too carried away when we went to Old Trafford a couple of weeks ago and won there.
"It was three points, it was a boost to confidence and it was terrific. It changed a desperately poor record for us there as well, our first win there for 26 years.
"But equally any side can go to Arsenal and get beaten, so I wouldn't start to think the result was a major shock all over Europe.
"You can get beaten, but what we have to do is fight back against Liverpool and try to win."
Villa will be without suspended England winger Ashley Young against the Reds.
Young has started all 19 of Villa's league games to date this season but will have to serve a one game ban for collecting his fifth yellow card of the campaign at the Emirates Stadium.
O'Neill had hinted going into the Christmas period that he may make changes, particularly with Liverpool having an extra 24 hours to recover from their clash against Wolves.
Striker John Carew, defenders Habib Beye and James Collins plus midfielders Nigel Reo-Coker, Steve Sidwell and Fabian Delph will come into the equation for a possible start.
Aston Villa 13/8, Liverpool 13/8, Draw 23/10