City had to settle for a point after failing to break down Town's 10 men following Alex Pritchard's 54th-minute red card.
Wes Foderingham saved well from Jay Emmanuel-Thomas and Sam Baldock, while centre-backs Troy Archibald-Henville and Jack Stephens were outstanding in repelling some threatening City attacks.
Home goalkeeper Frank Fielding had to make a fine double save from Michael Smith after 57 minutes but after that his side poured forwards, aided by some attacking substitutions, without conjuring up a finish.
Cotterill said: "We played well and deserved to win, but you have to credit Swindon for the way they defended.
"If there was a criticism it was that we didn't get a decisive head or a foot on the many dangerous crosses we put in.
"We started well, Swindon then got into the game, and after the sending-off we dominated. By the end we had a lot of attacking players on the park and just couldn't come up with the goal our play merited.
"A clean sheet was welcome and overall I was pleased with the performance. It's another game we can build on and another step in the right direction."