Barnes insists the former Fulham chief should be given time to mark his mark at Anfield.
"Getting on his back is not going to help the team," Barnes told talkSPORT. "That wasn't the wisest decision he made to criticise the fans, he should never do that. However, the fans should support him.
"Roy has to try and instil his footballing philosophy on the team. Coming to Liverpool after they have been used to Rafa [Benitez] for six years then all of a sudden for Roy to instil his ideas is going to take time.
"It's difficult all of a sudden to change it overnight. Yes they are not playing particularly well, particularly cohesively, but Roy has to be given time."