The Gunners saw their advantage trimmed after surrendering a 2-0 lead in a frustrating 2-2 draw with Wolves, who currently sit bottom of the Premier League.
The dropped points have reduced Arsenal's cushion to five points, with Manchester City lurking ominously behind and holding a game in hand.
Rice acknowledged that the team must respond swiftly to silence critics, as questions intensify over whether Mikel Arteta's side can retain top spot.
Arsenal are chasing their first league title in 22 years, having fallen short in recent campaigns.
The title race could hinge on April's showdown, when City - managed by Pep Guardiola - host the north London side.
"We're on our own journey, we're on our own path and we fully believe in each other," Rice told Sky Sports.
"We want to do it because we've got such a good core group, such quality players now that we can do it. It shows that we can flick a page in terms of people talking about that mentality.
"We need some perspective about where we are, but also we need to look a bit bigger to understand that if we carry on doing what we're doing in terms of the results, it isn't going to last.
"It's on us as players to pick that up because we have it in us to win every game. I genuinely believe with this group, with what we've done here before, we could go on the run and easily win games.
"But it's on us. We've got to be switched on. You're going to be ready for everything that's thrown at you because that's what is needed for these final games."