Shrewsbury boss Graham Turner felt one or two things went against his side at the County Ground but admitted that Swindon were worthy winners in the end.
After a lifeless first half, the hosts scored twice soon after the break with a penalty from Chris Martin and another goal from Andy Williams.
Disappointing Shrewsbury offered little as an attacking force but missed a penalty in the 83rd minute after Alan McCormack had fouled Jon Taylor.
On Swindon's penalty, Turner said: "I was amazed when the referee gave Swindon their penalty. Williams was already slipping when he clashed with Connor Goldson.
"But the two quick goals just after half-time knocked the stuffing out of us and the missed penalty at the end summed up our day.
"The dressing room was bitterly disappointed with Swindon's penalty but we did not defend well and did not work hard enough to retain possession.
"We were poor in the first half. We kept giving the ball back to Swindon and you do not get much time when a team as good as Swindon are closing you down."