Sale were outclassed by La Rochelle, who claimed a place in the Champions Cup semi-finals for the first time with a 45-21 victory.
Sam James' converted try just before the break saw the Sharks trail by just two points, but the hosts stretched away in the second half.
Raymond Rhule ran in two fine tries, and also set up Geoffrey Doumayrou to cross for the first of his own pair.
Sale's Byron McGuigan touched down for a late consolation try.
Sale started their first quarter-final in this competition in 15 years well, briefly leading early on when fly half AJ MacGinty landed a penalty that was quickly cancelled out by his opposite number Ihaia West.
The pair traded penalties again before West's clever chip was caught and fed on to Gregory Alldritt to allow the flanker to go over near the corner.
West's next penalty went over despite hitting the post, but after MacGinty's third penalty of the half the hosts extended their lead, Dillyn Leyds sprinting clear after taking the ball off the toes of Sale's Faf de Klerk.
The Sharks stayed in the game when centre James cut in to score his side's first converted try, and they trailed only 18-16 at half-time.
The two-point margin was as close as Sale got, however, with Rhule dummying his way through for his first try soon after the game resumed.
The Ghana-born South Africa international then took advantage when Sale full back Simon Hammersley misjudged a bouncing kick through, Rhule diving on to the ball over the line for another try converted by West.
Doumayrou's two tries put La Rochelle, currently second in the French Top 14, out of sight before McGuigan's late effort slightly reduced Sale's margin of defeat.
Teams
La Rochelle: Dulin; Rhule, Doumayrou, Botia, Leyds; West, Kerr-Barlow; Wardi, Bourgarit, Atonio, Sazy (capt), Skelton, Alldritt, Gourdon, Vito.
Replacements: Bosch (Bourgarit 75), Priso (Wardi 55), Joly (Antonio 59), Lavault (Sazy 66), Liebenberg (Gourdon 63), Berjon (Kerr-Barlow 72), Plisson, Aguillon (Botia 66).
Sale: Hammersley; McGuigan, S James, Van Rensburg, Yarde; MacGinty, De Klerk; Rodd, Van der Merwe, John, Wiese, Beaumont (capt), JL Du Preez, Curry, D Du Preez.
Replacements: Langdon (van der Merwe 64), Harrison (Rodd 55), Oosthuizen (John 55), Phillips (Wiese 67), Neild (J du Preez 67), Quirke, R Du Preez (de Klerk 58), L James.