The Gunners won 2-1 in Wednesday's (15.01.25) north London derby to move within four points of Premier League leaders Liverpool but the midfielder was disappointed that his team didn't win more comprehensively.
Rice told TNT Sports: "You could tell tonight meant more than anything. The first 45 minutes was just pure domination.
"We showed that intent, that pressure, that desire. You could tell it was a derby. To be honest, I think we are unlucky we didn’t score 10 today. That’s the feeling."
The result meant Arsenal completed a league double over their rivals this season and Rice savoured the special occasion at the Emirates Stadium.
He said: "You don’t need a message. When you play Spurs, you know what it means to the fans.
"If you’re a player and you can’t get up for Spurs, you shouldn’t be playing football. You need to have that fire in your belly. We had that tonight.
"In the second half, the game got stretched, they could have maybe scored a couple, but we could have had another five or six.
"That’s the disappointing thing, but to win is the most important thing. Hopefully, we can now go on a run because this is the most important part of the season."
Rice also praised Arsenal fans for their support of Kai Havertz - who was subjected to online abuse after the Gunners lost in the FA Cup to Manchester United last weekend.
Asked if the German is an unfair scapegoat, he said: "Yeah, definitely. But there’s a social media perception, and then when you actually come to the stadium and hear the real fans and what they think, it’s two different things.
"The cheer he got tonight was ridiculous, it was the loudest cheer of the night when his name got called out. You could tell that meant a lot to him.
"The way he fights and scraps for 90 minutes, he does it week in, week out. He might not score every week, but what he does for the team is the most important thing. He’s been brilliant for us."
