Mathias Doumbe's 58th-minute header and substitute Ryan Lowe's cool last-minute finish at stadium:mk handed the in-form Dons their third win in four games.
Tuesday night's win took them to within four points of the sixth-placed Robins, and Robinson said: "I thought we deserved that, we were the better side.
"To be fair Swindon are one of the best teams to have come here this year, with the way they passed and moved it they were a constant threat.
"But I don't think they created a chance of note. I thought we created two or three first half and two or three second half against a good side, so it was a good evening for us.
"We're in the mix now and we've got a big game away at Leyton Orient at the weekend, and that's going to be a big ask for everybody involved."