Tevez, who hit the winner on the night, was visibly upset with Allegri for substituting him late on.
Allegri sought to console the Argentine, says Sport, but the striker was having none of it.
As Tevez passed Allegri, he is alleged to have said "wimp" and "mother******", before taking his place on the bench.
The striker continued his tirade from the bench. But all was forgiven at the final whistle as Juve held on for the 2-1 win.