The rout at Anfield has seen them drop to second in the Barclays Premier League and on Wednesday they host Manchester United.
O'Leary, who spent 18 years at Arsenal, views leaders Chelsea and Manchester City as the favourites for the title.
"Arsenal were absolutely shocking," he told BBC Radio Five Live's Sportsweek programme.
"Per Mertesacker was found out. He's been steady and doing well, but was found wanting pace-wise.
"I'd love to be proved wrong, but Chelsea and Manchester City are the favourites. Jose Mourinho seems to get teams over the line.
"So the FA Cup is the one where you can see them cracking this long spell (eight years) without a trophy.
"That would be great and that's where I see them."
O'Leary also criticised manager Arsene Wenger's failure to sign a striker during the January transfer window to cover for Olivier Giroud.
"You might not get that big signing that you really want, but I thought that at least they'd improve their bench," O'Leary said.
"They've been trying to get rid of Nicklas Bendtner for ages and I thought they'd bring someone in who's better than him. I was very surprised by that."