Johnnie Jackson had given the Addicks the lead but Matt Ritchie equalised before Charlie Austin edged the Robins in front. Sean Morrison added a third before Austin bagged his second and Pawel Abbott netted a consolation for Charlton.
"The equaliser knocked us and I could feel the lads were thrown at half-time," said Parkinson.
"We said we can't let that happen, we've got to go again.
"It is responding and making sure we go again and I have to say the game was one where Swindon showed more desire in our box to get on the end of things.
"When the ball went in their box there was too many free headers by defenders."