Mbia was given his marching orders just 10 minutes from time, with his side in contention for a point at 0-0. However, moments after the sending off, the hosts exploited their one-man advantage and Mikel Arteta scored the only goal of the game.
The Cameroon international will now miss his side’s upcoming matches against Reading, Stoke and Southampton.
"I'm sorry about Saturday," Mbia wrote on Twitter.
"I've learned for next time. Thanks to fans and team for the support. Very focused for next important dates."
Hughes defended the Cameroonian after the match, claiming that he acted out of frustration at Vermaelen’s challenge and that there was only slight contact in his retaliation.
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"That's a frustration because the linesman has actually given a free-kick our way,” he told Sky Sports.
"Stephane was on the floor and he has swung the leg, there is very minimal contact and Vermaelen is going to make the most of that situation.
“He dives and rolls around, and makes sure the referee makes a decision. There is contact and it's a wild challenge.
“It's a sending off that has really hurt us at a point in time when we're making positive substitutions as there was a real opportunity to get three points."