Those cries intensified after Dave Worrall claimed a 54th-minute equaliser and ex-Rovers trainee Mike Jones sidefooted home an 81st-minute winner for League Two Bury.
That condemned Tranmere to their ninth defeat in 11 games, but Barnes said: "It's the fans' prerogative to start booing and calling for my head before the game starts. And if we're losing and not playing well then fine.
"But to still be on our back when the lads are 1-0 up and they're doing well - that was the disappointing thing. I've said to the players that the fans may be having a go at me and (assistant) Jason McAteer, but they've come here to support them.
"I don't think it's affecting the players because they didn't hide, they didn't shirk - and it certainly won't affect me. It won't stop me doing what I do on the touchline or at training."