Agard lifted Luke Freeman’s pass over Wes Foderingham after a sustained spell of pressure from Town for just his second goal since February 17.
Joe Bryan and captain Aaron Wilbraham netted inside the final 10 minutes to move City a step closer to promotion but it was the 25-year-old forward who was his manager’s focus.
“I am delighted for Kieran Agard because he has had a bit of a lean spell but his work-rate hasn’t diminished and I thought he was magnificent,” Cotterill explained.
“It always starts with your strikers and I thought those two absolutely deserved their goals.
“I was pleased for Aaron and his 19th of the season but I am probably more pleased for Kieran Agard because I just felt he needed a goal more than anyone else. I thought his performance was immense.”
City are now just six points away from promotion back to the second tier which means Saturday’s mouth-watering clash at Preston has even more significance.
“I thought it was important we won this game,” Cotterill added. “There is a big game at the weekend and it is important now we rest, recuperate and get down from this one for a really good game at Preston this weekend.
“We didn’t need that game in the second half to become ding dong and end-to-end. We worked on that on Monday and talked about it at half-time.”
An early red card from Wade Elliott blighted their 1-0 loss at the County Ground back in November and Cotterill said his squad knew to keep their cool in a fiery derby atmosphere, adding: “I didn’t have to say about discipline, they knew.
“We are second in the fair play table, second only to Walsall having played more games. That is something we are very proud of this season.”
Swindon’s second 3-0 loss in four days leaves them looking at a play-off place having previously been in the mix for automatic promotion.
Boss Mark Cooper was left to curse a string of missed chances, either side of Ben Gladwin rattling the crossbar at the end of the first half, and a fine display from City goalkeeper Frank Fielding.
They will now face Peterborough this weekend without Yaser Kasim and Raphael Branco after the pair picked up yellow cards.
“I thought we played quite well and played some really good football but when you get your opportunities you have got to put it in the back of the net,” Cooper said.
“We created a lot of chances and if you create that many and don’t score it makes it difficult. The goalkeeper has made a couple of brilliant saves, he’s managed to claw them out. But there were a couple we’d expect our strikers to score.
“We are just looking to prepare and have a good and hopefully exciting, end to the season.
“We’ve had four intentional breaks this season which is difficult at a League One club.
“We didn’t play for three weeks before Saturday and got seven players back on the Thursday before the MK Dons game which made it a fragmented preparation which has knocked us back a bit.”