The Gers missed the opportunity on Saturday after failing to beat Raith.
The Light Blues could have been promoted to the Scottish Premiership on Saturday but failed to beat Raith Rovers, who scored a last minute equaliser to earn a 3-3 draw.
While a draw in midweek will practically wrap the title up given the Gers' vastly superior goal difference over Hibernian, Warburton has told his players to go out and win the game, and in emphatic fashion.
"We should have been out of sight and we have to do the job on Tuesday night," he told The Scottish Sun.
"It's not about Hibs or Falkirk, it's about us.
"We want to win it full stop and we don't want to limp over the line."
Although the nine goals they have conceded in their last three games should ultimately have absolutely no impact on their promotion, Warburton will want his side to go into their two upcoming games at Hampden Park having confirmed the title is heading to Ibrox and confirming it with the kind of impressive win they were bagging almost every week earlier in the campaign.
With the opportunity to confirm the league crown, win the Challenge Cup and beat their Old Firm rivals - which would also result in them booking a place in the Scottish Cup final - all ahead in their next three games, the Gers boss will surely want to see a ruthless performance in their next game to give them plenty of momentum for the upcoming fixtures.