Dean Lewington was given his marching orders in the 40th minute for appearing to elbow Swindon's Simon Ferry as the Dons full-back attempted to take a quick free-kick.
Matt Ritchie was credited with the only goal of the game just before the break although Town striker James Collins claimed to have got the final touch to the former's centre.
"This was a big win for us although I did not completely enjoy the second half," Di Canio said. "MK Dons are an intelligent side and know what they want to achieve. They did not finish in the top six last season by accident. This was a real test for us against one of the best teams in the division. Even before the sending-off we were the better team.
"I do not know if the red card was for a violent reaction or if he wanted to keep the ball and put his elbow in hard.
"I am not sure who got our goal. Perhaps they can have half of it each."