Rice, who was already on a booking, nudged the ball away from Joel Veltman which led to his second yellow and sending off which arguably cost Arsenal three points.
It was the first red card of the England star's career which came as a shock for many but the board which reviews the big refereeing decisions in the Premier League each week agreed it was the right call.
"Rice knows what he's doing - it's a gentle touch, but once the referee sees it, he has no choice," said the panel.
The panel supported every on-field call over last weekend except the decision not to give Crystal Palace's Will Hughes a second yellow card in their 1-1 draw at Chelsea.
However, the panel did argue over this call.
"Palmer is the wrong side of Hughes and has options left and right, therefore it is stopping a promising attack."
Arsenal succumbed to Joao Pedro's leveller which earned Brighton a point at the Emirates, a point that could be crucial in the title race.
