Leicester boss Marcelo Loffreda offered no excuses after the double Heineken Cup winners were rushed out of Europe with indecent haste.
The Tigers, European champions in 2001 and 2002, have become England's first major casualty of a tournament Guinness Premiership clubs look like dominating this season.
London Irish, Gloucester, Saracens and holders Wasps are all queueing up to claim prized quarter-final places.
Leicester, though, must reflect on just a third pool stage exit in 11 European campaigns after being undone 17-12 by Andy Robinson's Edinburgh at Murrayfield.
Loffreda, who led Argentina to the World Cup semi-finals just three months ago, said: "Obviously, we are bitterly disappointed. We had three penalties in the last 10 minutes, yet didn't go for goal with a single one.
"This was a game we could have won, and if we had kicked a couple of goals in that period we could have put pressure on Edinburgh and the result might have been very different.
"But we were not surprised by Edinburgh - we expected them to be strong at home."
Tries by Ross Ford and Phil Godman saw Edinburgh avenge a 39-0 Pool Six drubbing at Leicester earlier in the tournament, and former England head coach Robinson said: "It was one of the best performances since I came to the club.
"And the fact it was against one of the strongest teams in Europe made it all the more special."
Toulouse, despite a 20-13 loss to Leinster in Dublin, will top the group if they subdue Edinburgh at home next Saturday.