Barnes makes the claim in his foreword for a new book, “Champions At Last".
Published in the Liverpool Echo, Barnes wrote: “Getting that support from the fans is vitally important because, subconsciously at least, the players can absolve themselves from responsibility if the fans are against the manager.
“I know how it works; the players feel it doesn't matter if they lose as the manager will take the flack from the fans.
“On the other hand, if the fans back the manager 100% then the players believe in the manager to such an extent that when the boss says jump, they jump because the players know the fans back the manager and the board back the manager.
“The importance of the fans shouldn't be underestimated. Clubs don't want to sack their managers, but if they lose the confidence of the fans and that transmits itself into the dressing room, then the club has little choice.
“That certainly was the case at Anfield when the fans turned on Brendan Rodgers, who deserved more time in my opinion. He went on to show what a good manager he is when he moved onto Celtic and now Leicester City, who were in the title hunt briefly this season.
“They didn't accept similar decisions by Brendan Rodgers, and if he left, say, Sturridge out of the team, they would let him know their feelings. “The Liverpool fans believe in Jurgen Klopp. When he makes a decision, such as he did about Daniel Sturridge for example, the fans accept it.
“They didn't accept similar decisions by Brendan Rodgers, and if he left, say, Sturridge out of the team, they would let him know their feelings. "