The England midfielder helped Arsenal secure a 1-0 win thanks to an early Bukayo Saka strike.
The Gunners had to employ every trick in the book to halt their hosts’ rhythm and saw David Raya save well from Georginio Rutter as they created very little themselves.
Speaking at the London Football Awards, Rice said: “There have been times where we have won, played really well, but it has not felt as good as winning probably last night when we played Brighton.
“We know we didn’t play well and to win 1-0 there, in a place that has been tough for us in recent years, means that little bit more.
“We have just got to keep winning matches, take it one game at a time and keep focusing on ourselves.
“If you start focussing on other things, it’s not going to happen.”
Rice sidestepped a question about criticism from Albion head coach Fabian Hurzeler about their tactics.
He said: “Ever since I’ve been at Arsenal there is noise every week.
“That’s what come with playing for Arsenal.
“People are going to like parts of your game, people are not going to like parts of your game.
“But the main thing is winning. You can win ugly, you can win playing well.”