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The Iron faltered while the home side became more adventurous, with Christian Roberts converting a late penalty - given after a handball by Ian Baraclough - to earn the Robins a point.
Laws said: "I am disappointed, we were dynamite in the first-half and controlled it.
"We were disappointed that we only had one goal, we had enough chances to get a couple more.
"We started the second-half like we finished the first, but the red card was the turning point.
"We never used that extra man, they got bolder and caused us more problems.
"In the end we could have lost, we were hanging on. We were our own worst enemies and it's a poor result for us."
Swindon caretaker boss Iffy Onuarua criticised Fallon, who now faces a three-game ban for violent conduct.
He said: "It was minimal contact but it was always coming. I expect better of him, a straight red for a two footed lunge is obvious serious foul play but Rory's was disappointing.
"The service was poor to him but he's got to be big enough to realise it's not going to be perfect every time.
"I'd like to replay the second-half of this game against Huddersfield next week.
"We were sluggish at the start but once we were down to 10 men the shackles came off and we played well."