The 24-year-old was dismissed following Barrie McKay's goal which put the Scottish Championship leaders 2-0 ahead.
The Scottish Sun reports that the 24-year-old was shown a second yellow card after gesturing to supporters in the wake of Barrie McKay's goal which essentially clinched the game for the Scottish Championship leaders.
But Warburton was furious with the decision, and issued a sarcastic response to highlight his confusion over the incident.
"I've been told our player was sent off for making an offensive gesture which incited the Morton fans. I've seen it and the player made the fatal mistake of celebrating a second goal. It was scandalous behaviour on his part," he said, as reported by The Scottish Sun.
The sending off was the only negative during an important victory for the Light Blues. The three points restored their five point advantage at the top of the table.
But with the win virtually assured by the time Barry Cook produced the second yellow card, it is understandable as to why Warburton's mind switched to the dismissal.
Because Halliday was sent off for two yellows, he will be unable to appeal the decision (via The Scottish Sun), meaning that he will definitely miss the club's clash with third place Falkirk at Ibrox on Saturday.