Rice found the winner for Arsenal seven minutes into injury time on Tuesday night.
He said, "Luton are a top side. They can't be overlooked in this league because of the quality they have. They made us pay on set pieces.
"We have to take it every game as it comes. They were eight points clear last season. We have new players like me coming in and learning. It's just about us and not worrying about anyone else and getting three points each week.
On the winning goal, Rice added: "I went off his back should and attacked it. Anything can happen. Those are the moments you look back on. What a game. to score the winner is an honour."