"I think we said after last week (defeat by Manchester City) that we have to win five games if we want to win the Premier League," he said.
"That's one down and now four to go. It was about winning no matter how we win."
Stuttering Arsenal have seen a nine-point lead in the title race evaporate, and last Sunday's 2-1 loss at Manchester City, combined with City's narrow win at Burnley on Wednesday, dislodged them from top spot for the first time since October.
Saturday's victory, sealed by a majestic ninth-minute goal by Eberechi Eze, was hard going, but crucially it put Arsenal three points clear again, although City have a game in hand.
With Arsenal's and City's goal difference virtually the same, the race has turned into a five-game sprint, and Mikel Arteta's side must now focus on their remaining league games at home to Fulham and Burnley and away to West Ham United and Crystal Palace - hardly the most formidable fixtures.
Win all of those, and they would have a great chance of delivering a first league title since 2004.
"It is exciting times. There's a lot to play for," added Rice, who will be back leading the midfield away to Atletico Madrid in a Champions League semi-final first leg on Wednesday.
Arsenal's players looked out on their feet at the final whistle after 97 minutes of hard graft. But captain Martin Odegaard promised there would be no let-up in Arsenal's bid to keep City at bay.
"This schedule is crazy. We just have to keep going. It is the end of the season, just leave everything out that we have inside, fight every single game, and we just have to keep going," the Norwegian said.
"That's where we want to be, but it is going to go all the way to the end.
"We are ready for it, and we will fight every single day."