Alessio Cerci missed a stoppage-time penalty as Torino were denied a place in next season's Europa League following a 2-2 draw with Fiorentina.
They headed into the game in the final European position, but Parma claimed a 2-0 win over Livorno to pip them to sixth place in the Serie A table.
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Giuseppe Rossi almost gave the hosts an early lead when his curling effort from the edge of the box was tipped over the bar by Daniele Padelli.
Torino had a sight of goal when Jasmin Kurtic powered in a strike, but it was well held by Antonio Rosati.
At the start of the second half Alberto Aquilani was inches away from breaking the deadlock when his near-post header from a corner drifted just wide.
Minutes later Fiorentina were awarded a penalty after Giuseppe Vives brought down Juan Cuadrado inside the box. Rossi stepped up to take the spot kick and placed a low effort into the bottom corner to take his tally to 16 goals in Serie A this season.
Torino drew level in the 67th minute when Cerci's ball across the box was slotted in from close range by Marcelo Larrondo.
The visitors thought that they had taken the lead six minutes later after Emiliano Moretti found the back of the net, but the goal was disallowed for a foul in the build-up.
Torino pushed for a second goal, but they were caught out on the break and fell behind again in the 79th minute.
Cuadrado led the charge with a driving run towards the box, before feeding the ball into the path of Ante Rebic to fire a strike into the roof of the net.
Five minutes later Torino levelled the scores for the second time as Kurtic fired a free kick from just outside the box into the top corner past Rosati.
Torino were given the chance to win the game in the third minute of stoppage time when Facundo Roncaglia brought down Paulo Barreto in the area.
Cerci took the spot kick but saw his effort saved by Rosati as the game ended in a draw, enabling Parma to snatch the final spot in Europe.
Alex Meyers
