Rice saw a second yellow card on 49 minutes for interfering with a Brighton free-kick.
It was Rice's first-ever dismissal and he said: "I was shocked, I think you could see in my face I was shocked. He's (Joel Veltman) 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.
"I have to move on from it, I will be better for it and I can only praise the players for digging deep for me, and the manager for pushing everyone, and the fans as well who were unbelievable again this afternoon. That's how I see it."
Rice also said: "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. I'm sure this group of players, me and everyone else, we're only going to strive towards one thing and that's to be successful.
"We'll keep going, I know it's tough, it's tough for me as well but we'll be back stronger, and we know we've got a tough set of fixtures when we are back from the internationals, we'll be ready. Stick behind us, your incredible support is what we need."
