Gary Kinsella had given the non-league team the lead after 30 minutes of the pre-season friendly, giving new loan signing Luke Daniels no chance as he smashed home from close-range.
Tranmere fought back with strikes from Alan Mahon, Ian Moore and Ash Taylor, but Barnes picked out keeper Daniels for special praise.
"We played well in the first 15 minutes but then we became lackadaisical," he told the club's official website. "We stopped moving the ball quickly and we started to be sloppy.
"We had a chat about it at half-time, we started to play one and two touches again and created more problems for Southport.
"Luke was very impressive in training and in the game. You can see he's a commanding goalkeeper and a good shot-stopper."