Victory would see the Scottish Cup finalists draw level on points with The Bairns, who currently hold second spot.
Both are at home on Sunday - Hibs to Queen of the South, Falkirk to Morton - but Falkirk have a superior goal difference of +26 to Hibs' +19.
"If anything there is a lot more pressure on Falkirk now," Stubbs said.
"It is amazing how it flips round. It is all against us now to score eight goals (over their two games), and even if we did, that doesn't take into account that they might score more to add to that.
"We have to think that Falkirk are going to win their game but it is all to play for.  There will be a real pressure on them to win and it won't be easy against Morton.  As you saw on Saturday, they are a well organised team."
Hibs' failure to win at Cappielow means Falkirk are in pole position to claim second spot, which would put them straight into the promotion play-off semi-finals.
If Hibs have to settle for third, they would need to negotiate a quarter-final play-off against fourth-placed Raith Rovers, with the first leg next Wednesday, 4 May, and the second on Saturday, 7 May.
"I have said all along, playing extra games is not going to affect us because we have played extra games anyway," noted Stubbs, whose side could play another seven games after the end of the regular season on Sunday, including the Scottish Cup final on 21 May.
"We had 10 days' break last season (before the play-offs) and it didn't necessarily help or hinder us.  Some people say if you win the two extra games, then you go into the next two with confidence and momentum.
"The most important thing is we have to win the game on Tuesday, first and foremost.  If we can make inroads into the goal difference after that, fine, but it isn't as easy as that unfortunately.
"If we win, there is no pressure on us going into Sunday.  All the pressure is on Falkirk because they desperately want to finish second."
Hibs have only scored more than three goals twice this season, although one of those was a 4-2 home win over Dumbarton back in October.   But they lost both away games to The Sons, who are already safe from relegation.
Stubbs has defender Liam Fontaine available again while midfielder Dylan McGeouch could return on Sunday against Queen of the South, with Danny Carmichael also likely to be back for the play-offs.
Hibernian manager Alan Stubbs says "all the pressure will be on Falkirk" if his side beat Dumbarton on Tuesday ahead of the final round of Championship games.