Referee Lee Miller first suspended play at 3-0 to Rovers with the waterlogged Valley pitch affecting play.
Paul Keegan, who was later sent off for two yellow cards, opened the scoring in the second minute before a Chris Brown double gave the south Yorkshire side a three-goal lead all inside 22 minutes.
But the players were taken off the pitch just before the half-hour mark, before returning and playing until the break when the match was called off.
And Rovers boss Paul Dickov said: "I'm disappointed obviously. We were playing some really good stuff, so the referee to suspend play was disappointed.
"Then 15 minutes later it was no worse. Because of the way he has done it it's shambolic.
"As a spectacle my team were fantastic and caused problems. Charlton then started to get the ball down and pass it
"I didn't see one bad tackle and both sets of players deserve credit and wanted to continue.
"The referee could have let the game go on longer. I thought we were fantastic for 30 minutes. He should have let play go for as long as he could before half time - once he made the decision to take us off, he put a whole lot of pressure on himself. It's a tough decision for him to make.
"The pleasing thing for me is the more we play the better we get. If it stands and the goals and results don't it has to be the worse decision ever and such a contradiction. It's something we have to look at. "
Simon Church replied for Chris Powell's side as they got back into the game with his second in as many Championship outings.
And Addicks boss Powell said he was pleased with his players' reaction.
He added: "I think my players responded to the position we were in.
"Who knows what could have happened, but we should never have got ourselves in that position. They showed a bit of bravery.
"I know Paul will be despondent and rightly so as if I was in his position. But we were ready to go out.
"There were problems on one side, but there were two teams out there that scored four and I'm sure many of us would say a few years back you would carry on."