A 3-1 defeat at Blackburn Rovers on Wednesday was Liverpool's ninth in the Premier League this season, leaving them in 12th place and just four points above the drop zone.
Keegan knows a thing or two about the demands of club management, not to mention carrying a nation's hopes on his shoulders as England manager, and he rolled his eyes to the ceiling when quizzed on Hodgson's predicament on Thursday.
"If you win and play terrible everything is okay, if you lose and play well it's a massive problem," Keegan told Reuters on behalf of broadcaster ESPN at Chelsea's Stamford Bridge - just a few rooms away from where under-pressure Chelsea manager Carlo Ancelotti is plotting to get the champions' season back on track.
Keegan said he sympathised with Hodgson, saying the 63-year-old Englishman was in danger of becoming the fall guy for years of decline at the club.
"You have to look way beyond Roy Hodgson to see where things started to go wrong at Liverpool, the decline has been going on for at least six or seven years, maybe longer," he said.
"The problem is because of the history of the club and the expectations of the fans the bar is too high for the players that are there at present. The players that are there can't live with the standards that have been set in the past."
John Barnes, part of the last Liverpool team to win the league title, said Hodgson, appointed in July last year, had been brave to take the job in the first place after Rafa Benitez was sacked.
"He was the right man for the job because I don't believe any other big name manager would have taken the job on," Barnes, who dipped his toe into the murky world of club management with Celtic and Tranmere Rovers, said.
"Yes, Alex Ferguson would have been better, Arsene Wenger would have done better and Jose Mourinho would have done better but they aren't going to Liverpool and put their reputations on the line.
"In terms of who would be willing to put their reputation on the line knowing you are not going to win the league or finish in the top two or three then Roy was the right man."
Hodgson is just one of a number of Premier League managers under intense pressure to keep hold of their jobs.
Chris Hughton and Sam Allardyce were shown the door by Newcastle United and Blackburn Rovers just before Christmas and the New Year cull could be even more brutal.
Even the prospects of Chelsea's double-winning coach Ancelotti look bleak after a demoralising run of one win in nine league games, culminating in Wednesday's 1-0 defeat at Wolverhampton Wanderers.
The back pages of most papers have the Italian well positioned in the so-called "sack race" although West Ham's Avram Grant and Aston Villa's Gerard Houllier are also jostling for the lead in a macabre dash to the exit door.
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Try your first month for just £1 / $1 / €1