In a fiercely contested match Jim O'Brien gave the visitors the lead in the 25th minute only for Tom Ince to level things after the break.
The game turned in Barnsley's favour when Blackpool goalkeeper Matt Gilks saw red for handling outside the box just after the hour, before Jason
Scotland popped up with the winner two minutes from time.
"I can't ask for any more from the players," Thompson said.
"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 10 we have to react to the situation.
"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."