Villa were denied a last-minute equaliser after Ollie Watkins' goal was overturned for offside, with replays showing the finest of margins.
Rice said after the game: "Luckily he's offside. Small margins. To come away with three points, we've got to be happy.
"I think all the players were discussing this on the pitch. The longer it takes, it feels the decision will go the other way. If it's made quickly then it's a goal. We knew it was going to be offside.
"I'd be gutted [if that happened to Villa]. We had it last year at Sheffield United when I parried the ball with my arm.
"The lads are laid back about it. Some weeks we get decisions, some weeks we don't. There need to be tweaks. There needs to be a change but I don't think they'll change it mid-season."