Rovers supporters chanted 'Barnes out' before police moved them on their way following a defeat which leaves them second-bottom in League One.
Chris Shuker put Tranmere in front, but goals from Darren Byfield and Troy Deeney turned the game on its head.
Alan Mahon levelled for the home side but Deeney struck late on to give the visitors all three points and Barnes said: "We've got to stop conceding goals and at the moment we don't look like doing so.
"I can understand the fans' frustrations. I'm frustrated and so are the players. But I'm not taking responsibility for everything. The players must stand up and be counted. We made some bad decisions and experienced players should have done better.
"We didn't show much quality, although we showed plenty of fighting spirit. I still believe in the players but they don't seem to believe in themselves. We started well and scored a good goal but really it was slack play by us all afternoon. We seemed to give goals away when we are in possession and I just can't understand how."