Last year's beaten county finalists were eliminated following a 3-14 to 1-18 defeat against Templederry in Dolla.
Nenagh seemed to have pulled the match out of the fire when Billy Heffernan's 56th minute goal put ahead for the first time in the game.
However, Templederry hit back and Adrian Ryan goaled in second-half stoppage time to sent them through to the knock-out stages.
The draw for the quarter-finals was made shortly after that match concluded and threw up the following pairings:
Templederry V Lorrha or Roscrea
Burgess V Borrisokane
Kilruane McDonaghs V Borris-Ileigh
Kildangan V Portroe or Ballina
Those ties are due to be played on the weekend of the 25th and 26th of June.
