Instead, the French Championship leaders claimed a bonus point of their own to move to 15 points in Pool Three while Ospreys are second on 14 points.
However, bonus-point victories in their remaining two matches - away to Italian minnows Calvisano and home to Ospreys - could yet secure Sale an improbable quarter-final spot.
Saint-Andre said: "We will try to get five points in the next two games.
"We go away to Italy and then we'll play the last game against Ospreys. We'll also see what happens when Stade Francais go away to Ospreys.
"I ask my players never to give up and we've won here and we'll fight until the last game."
Sale at least secured victory here to keep their hopes alive, but failed to exact true revenge for their 27-16 defeat against Stade in Paris last Sunday.
Lee Thomas, who impressed at fly-half after being given the nod ahead of Daniel Larrechea, kicked three penalties and Chris Bell added a drop-goal midway through the opening period.
Sale failed to build on their 12-0 advantage, however, and never really looked like penetrating Stade thereafter.
A first-half penalty from Lionel Beauxis was added to late in the second half by another penalty from David Skerla to hand the Parisians a bonus point.
Saint-Andre added: "We lost the points last week in Paris, but I'm pleased to beat Stade Francais.
"The commitment of the guys, and our defensive organisation, were good and Lee Thomas did well in what was his first time at fly-half in a big game like this.
"We are missing 12 to 13 players through injury it makes things difficult but we dug in for the win and will keep on fighting."
Stade boss Fabien Galthie was delighted to have secured a potentially priceless bonus point.
He said: "It was important that we got the bonus point.
"Sale scored a lot of points quickly and that made it difficult for us, but we knew that they would be very aggressive.
"It's important for us to make sure that we get into the quarter-finals."