After losing 2-0 at home and severely denting their title ambitions, Arsenal admitted there must be an inquest.
Rice told BBC's Match of the Day: "It's very disappointing. It's gutting, to be honest with you because of the chances we had in the first half to kill the game off.
Even though they hit the post at the end, we could've had two or three before that. When you don't take your chances against teams like Villa who have got quality, it can come back to haunt you in the second half and it did.
"It is the Premier League. It is why you need to stay focused for 100 minutes. The spaces we had in the first half weren't there in the second half, they were taking their time with everything and really frustrating us, of course.
In the end, they've scored two goals and completely killed us off. It is one of them days. It happens in football. It is about rolling our socks up and going again.
"I didn't know they got beat. My phone was off before the game, I didn't check the scores or speak to anyone because we can only control what we can do. I don't worry about the other teams. Obviously we didn't control that today which is obviously annoying but we've played last before and it's not been a problem so I don't think any of that really matters to be honest.
I think it's just down to us, we can't put it down to that. I think us as players, we need to look at ourselves and see why we didn't win the game and why we switched off for two or three minutes, which has killed us. It's disappointing, but now there is the chance for a big reaction on Wednesday night and then away at Wolves. We're going to need to be right at it."