Sale, champions in 2006, face league leaders Bath at Edgeley Park on Friday night.
And Saint-Andre believes five wins are required from the last six Premiership games to guarantee a top-four finish.
After Bath, Sale face trips to Bristol and Wasps, before hosting Newcastle and London Irish either side of visiting current fourth-placed team Harlequins.
The Sharks will go above Quins if they beat a Bath side that moved top courtesy of a narrow victory over Irish last time out.
Saint-Andre said: "Competition for the top four is intensifying by the week.
"We need to win five out of the last six games to make sure of a top four place.
"Bath beat us at their ground with the last kick of the game earlier this season, and my players still remember that.
"Bath have been among the Premiership leaders all season, and we will respect them throughout the game tomorrow evening.
"We beat top-of-the-table Gloucester a fortnight ago, and a win is our only objective."
Sale will be without England prop Andrew Sheridan because of an elbow injury suffered in training, although he is expected to be fit for next week's European Challenge Cup quarter-final clash against Brive.
New Zealander Luke McAlister, meanwhile, is on the bench after picking up a knock in training, but Scotland flanker Jason White returns as captain.
Bath head coach Steve Meehan makes several changes from the side that accounted for Irish, notably at fly-half, where Shaun Berne replaces Olly Barkley, and there is also a start for Tom Cheeseman in midfield.
Up front, England prop Matt Stevens switches from tighthead to loosehead instead of David Flatman, and the highly-rated Chris Goodman starts at number eight.
Meehan said: "We've got to a stage where there are a couple of guys who have pretty much been running covered in Band Aids.
"We have had our eye on those guys and have been a little concerned about them from a fatigue point of view."