Pep Guardiola's Premier League leaders, Manchester City, were beaten for the first time this season at Anfield as goals from Alex Oxlade-Chamberlain, Roberto Firmino, Sadio Mane and Mohamed Salah gave the hosts, Liverpool, a thrilling victory.
Kevin Keegan said Jurgen Klopp's side had the attacking quality to progress deep into the Champions League this season, but added that the squad was still not at the level required to mount a Premier League title challenge.
Liverpool face Portuguese side Porto in the first leg of the Champions League round of 16 on 14 February.
"Don't forget they are still in the Champions League, they could win that," Keegan was quoted as saying by the Liverpool Echo.
"Why not? They are in it. They have Porto next which won't be easy. But it's a tie they could come through.
"At the moment I think all the top teams in there have a problem of one kind or another. Are Manchester United better than Liverpool? Probably not. Are Chelsea? Probably not."
He added: "[To win the Premier League] Liverpool need to be able to hold on to their best players. Liverpool can't possibly win the league if they keep selling their best players to Barcelona."
Keegan expressed admiration for Klopp sticking to his attacking principles and hailed the signing of Virgil van Dijk from Southampton as a major coup for the Merseyside club.
"I think Jurgen fits like a glove," he said. "He gets the Liverpool humour, he gets what the fans want.
"He comes with a great track record, You can't argue with what he achieved at Dortmund.
"I enjoy watching this Liverpool team. What people have to understand is that if your best players are inventive and Liverpool's are then your strengths are at the front.
"Van Dijk is a very good defender and that signing may give them a solidity at the back which they haven't had before."