After going 68 Premier League games unbeaten at Anfield, Liverpool have slumped to back-to-back losses at the stadium that was their impenetrable stronghold for nearly four years.
The latest defeat - 1-0 to lowly Brighton & Hove Albion - left the champions' title defence on the brink of collapse.
Jurgen Klopp's Reds are seven points behind leaders Manchester City - who have a game in hand and are on a nine-match winning streak in the league.
City are the next visitors to Anfield, on Sunday.
A win for Pep Guardiola's team may effectively knock Liverpool out of the title race - with more than three months of the season remaining.
"The only explanation now is that we are a fatigued team," said Klopp, whose squad has been ravaged by injuries this season, especially in defence.
"City are flying and we have to find solutions."
Seeking to regain the title they relinquished to Liverpool, City produced another dominant display in overwhelming Burnley 2-0 at Turf Moor with Gabriel Jesus and Raheem Sterling scoring the first-half goals.
That restored City's three-point advantage over Manchester United - with Leicester City back up to third courtesy of a 2-0 win at Fulham courtesy of goals to Kelechi Iheanacho and James Justin.
While City have conceded just two goals in their past 13 league games, Liverpool are unlikely to have defensive leader Virgil van Dijk back this season while they weren't helped by goalkeeper Alisson Becker missing out against Brighton because of illness.
The title might soon be gone for Liverpool, and a place in the top four is hardly guaranteed.
The Reds are fourth, two points ahead of fifth-place West Ham United who were 3-1 victors at Aston Villa.
The Hammers took the lead through Tomas Soucek while Jesse Lingard scored twice on his debut for the club after his move from Old Trafford, either side of Ollie Watkins' reply for Villa.
"If he keeps up the form he showed tonight - and he is not completely match fit - and is scoring the goals, he will help us no end before the summer," Hammers manager David Moyes said of Lingard.
Everton are two points behind West Ham in sixth after beating Leeds United 2-1.
Gylfi Sigurdsson's ninth-minute strike and a header from Calvert-Lewin in the 41st gave the Toffees a buffer before Brazilian winger Raphinha replied for Leeds.