Paris - Stade Francais secured the bonus-point victory they needed over Leicester on Sunday to storm into the European Champions Cup quarter-finals, thus eliminating Ulster.
Parisians Stade ran in five tries to Leicester's three in a 36-21 victory that will likely see them face a trip to the Tigers in the last eight.
Ulster had kept their knock-out stage hopes alive on Saturday with an eight-try 56-3 rout of Oyonnax.
But a 22-10 bonus-point victory for Northampton at Scarlets on Sunday night, followed by Stade's win, means no Irish province has reached the quarter-finals for the first time since the 1997/98 season.
Munster were eliminated two weeks ago when losing at Stade while Leinster had already bitten the dust before the turn of the year.
Tries from flyhalf Jules Plisson, Fiji wing Waisea Nayacalevu and prop Rabah Slimani before half-time had Stade in control leading 19-7.
Back-row forward Raphael Lakafia scored the crucial fourth try on 54 minutes while South African flyhalf Morne Steyn rounded off the tries in the final minute.
Leicester were actually first on the scoreboard through centre Manu Tuilagi but Stade already had their bonus point before lock Dominic Barrow and hooker Harry Thacker crossed the whitewash.
Leicester had already won Pool 4 but with a bonus point victory they could have challenged Saracens for the top seeding.
As it is, they finish the group stages as the second seeds having lost their perfect record in Paris and they will now play either Stade, Northampton or the second-placed finisher from Pool 2 -- either Clermont or Ospreys.
The Welsh region are the last remaining hopes to prevent a quarter-final line-up comprising only English and French teams.
In the other Pool 4 match, Munster cruised to a 28-5 victory at pointless Treviso.
On Saturday, champions Toulon scraped into the quarter-finals with a tough 19-14 victory at Bath.
However, Wasps snatched top spot in Pool 5 with a bonus-point 51-10 thumping of Leinster.
It means Toulon will play Pool 3 winners Racing 92 in the quarter-finals.