Cooper left the likes of Nile Ranger, Dany N'Guessan and Wes Foderingham out of his starting line-up.
Cooper said: "It was good in that we managed to change a few things around and still get through the tie.
"It wasn't our most scintillating performance but Plymouth made it difficult for us.
"I thought we could have been three or four goals to the good in the first half. It was a good finish by Ajose and the first goal was outstanding as well."
The only downside for Swindon was the sight of goalscorer Barthram being carried off on a stretcher midway through the second half.
Cooper said: "We think Jack has strained an abdominal muscle after slipping. It is probably too early to say how long he will be out for."
- Sports & Recreation
- Wes Foderingham
- Nicky Ajose
- Andre Blackman