Crawley snatched a fortuitous winner three minutes from time at the Keepmoat Stadium when a shot from Josh Simpson deflected off the boot of Nicky Ajose on its way into the net.
Barker said: "I thought we were by far the better side in the last 20 to 25 minutes and deserved to win the game. I was extremely proud of all of them.
"Defensively we were fantastic and we got stronger as the game went on, whereas Doncaster started to look tired.
"They were a threat at set-pieces, but we worked hard to stop them getting crosses in and tried to play down the side of them because they had some big defenders.
"I set the players a challenge of not getting beat twice in a row and they've responded. I thought we showed we can play a bit and win a bit ugly as well."