The Sharks' lingering quarter-final hopes finally disappeared thanks to a 15-0 home defeat by Biarritz, who will face another do-or-die clash with Leinster in the south of France next Saturday to determine the winners of pool three.
Leinster, who were 32-6 winners over the Frenchmen in Dublin, could still go through if they lose in Aguilera but prevent their opponents from scoring four tries and secure a bonus point themselves.
Sale, meanwhile, are left to concentrate on domestic matters after suffering a second successive home defeat.
Having had their appetite for Europe whetted by a series of encouraging displays, the Sharks are more determined than ever to qualify for next season's Heineken Cup, either through the Zurich Premiership or the Powergen Cup in which they have reached the last eight.
But injuries are taking a heavy toll on Mallinder's men, who went into the game without six regulars, including fly-half Charlie Hodgson and prop Andrew Sheridan, and lost scrum-half Bryan Redpath before half-time with a suspected dislocated shoulder.
"When you are playing a top European side, you have to be as close to full strength as you can," said Mallinder. "Losing Charlie last week was probably the turning point of our campaign. We were excellent in the first 30 minutes against Leinster.
"But we can take a lot of positives from today's performance. Our set-piece was outstanding and we played some good rugby. We went out in a very positive frame of mind but I was very impressed with Biarritz's defence."
The visitors made a dream start, with Test full-back Nicolas Brusque grabbing a try after only two minutes, and, although they had to wait for another 44 minutes before prop Denis Avril was driven over for the clincher, they remained in control throughout thanks to a brilliant defensive effort led by France flanker Serge Betson.
"There are not many players at the moment in the world up to his level Neil Back is one but the good thing about today was that Serge didn't have to cover up other people's mistakes," said Biarritz coach Patrice Lagisquet. "Everybody put the tackles in.
"We noticed that Sale have started to play a wider game and it was important that we didn't get players sucked in. We kept our concentration collectively."
SALE: Robinson, Mayor, van Straaten, Bond, Hanley, Baxendell, Redpath, Yates, Cairns, Turner, Fullarton, Schofield, White, Sanderson, C. Jones. Replacements: Going for van Straaten (57), Wigglesworth for Redpath (38), Roddam. for Cairns (77), Stewart for Turner (55), Day for Fullarton (51), Lund for Schofield (48).
Biarritz scorers: Tries - Brusque, Avril. Cons: Yachvili. Drop Goals: Peyrelongue.
BIARRITZ: Brusque, Vidave., Stcherbina, Isaac, Marlu, Peyrelongue, Yachvili, Balan, Gonzales, Avril, Manent, Couzinet, Betsen, Tonita, T. Lievremont. Replacements: Gaitan for Stcherbina (77), Bernat-Salles for Isaac (77), Fitzgerald for Balan (67), Puleoto for Couzinet (70), Chouchan for Tonita (50).
Ref: A Roland (IRFU).