The Seasiders fell behind to Jim O'Brien's first-half strike but had the momentum when star winger Thomas Ince levelled shortly before the hour mark.
However, the red card shown to goalkeeper Matt Gilks swung the game once more and two minutes from time, Jason Scotland popped up to seal a welcome away victory for the Tykes.
Thompson said afterwards: "I can't ask for any more from the players.
"It was disappointing for me that the two Barnsley goals came about following our corners - that certainly doesn't help you - but the sending-off changed the whole complexion of the game.
"I've spoken to Matt Gilks and he had a real decision to make. He came out to meet the lad, the ball has hit his rib and then struck his arm but he certainly didn't mean it.
"We're just in need of a bit of lady luck. It definitely wasn't a blatant handball but once we've gone down to ten we have to react to the situation. The pitch was poor again, but young Mark came in and did well between the sticks.
"We still couldn't shut up shop once we'd lost a man though. The plan was for us still to go for the win of course, but I guess that's just how things are going for us at the moment.
"We're not in a relegation battle yet, but it's getting to the stage where we need the big characters to start standing up to be counted."