The Reds saw their inability to keep the back door bolted come back to haunt them once again in a meeting with Sevilla on Wednesday, as the Spaniards left Anfield with a 2-2 draw.
Roberto Firmino’s penalty miss did Jurgen Klopp’s side few favours on the night, but it was their ongoing struggles at the back which ultimately cost them two priceless points.
Keane believes that Liverpool have enough going forward to see them into the knockout rounds, but has warned that the very best are unlikely to fear a disjointed outfit as the battle for continental supremacy intensifies.
The Manchester United legend told ITV: "It's the easiest part of football: switching on.
"Liverpool do the hard things really well in terms of creating chances, pace, power and a bit of quality going forward. But that is the easiest part of football, yet Liverpool cannot seem to do it.
"Win the league and Champions League? No. Forget about it. I think they have enough to get through the group but later on against Real Madrid and all the big boys, they'll be laughing at Liverpool."
Ben Yedder opened the scoring for Sevilla on Merseyside, while Joaquin Correa struck a 72nd-minute equaliser.
Keane believes the second effort from the visitors encapsulates Liverpool at the moment, with the Reds defence reduced to a spectator role as they were carved open.
The Irishman added: "This sums up Liverpool in a nutshell and why they are not going to win any big prizes: the switching off from a throw-in and it leads to an equaliser in such an important game.
"Experienced players just switching off.
"They must drive the manager crazy because that is schoolboy defending - from a throw-in!"
Klopp’s side will then be heading out on the road in their next European fixture, with a trip to Spartak Moscow awaiting them on September 26.