The Gunners took a narrow lead into the interval after Kai Havertz opened the scoring with a clinical lobbed finish.
Arsenal may have been well placed at the half-time break, but the Emirates Stadium was left stunned when Rice was given his marching orders in the opening stages of the second period.
After being shown a yellow card in the first half, Rice received a second yellow in the 49th minute following a controversial incident.
Brighton defender Joel Veltman rolled the ball against Rice after being fouled by the Arsenal midfielder near the corner flag.
Rice flicked the ball away before he fell to the ground after being caught by Veltman's wild kick, causing the Arsenal players and fans to call for the Brighton man to be sent off.
Rice expresses shock at Brighton red card
However, it was Rice who was shown the red card as referee Chris Kavanagh ruled that he had delayed the restart by kicking the ball away.
Speaking to Arsenal's media channels, Rice admitted that he was "shocked" to receive what he felt was a "harsh" red card.
"I was shocked, I think you could see in my face I was shocked," Rice said. He's obviously gone over... I've not sprinted back in front of him and smashed the ball away.
"I've touched the ball with the outside of my foot. But look, this is the laws of the game. If you touch ball away, even a little bit, obviously it's a red card after my challenge in the first half which I fully accept was a 50-50 that I didn't win.
"But the second half one, especially with it being in the corner flag, they can't really progress anywhere from there. It was tough, it was harsh, but it's one of those things.
Rice apologises for sending off
While Rice may have felt hard done by, he has taken the opportunity to apologise to his teammates and Arsenal supporters after receiving the first red card of his career.
Rice added: "I think from my behalf, that's my first sending off in my career, so I just wanted to apologise obviously to my teammates, which I've done, and to the fans.
"When you get sent off, it's never nice, you get a sense of guilt over you, and I was lucky today that my teammates really helped me out and we didn't lose the game.
"I'll learn from it, I really appreciate the fans' support as always - it's not in my nature really to get red cards, so I'll learn from it, I'll see where I can be better, and I'll be back for sure."
As a result of the red card, Rice will be suspended for the North London derby against Tottenham Hotspur on September 15.