Allegri, who has just led Milan to their first Serie A title in seven years, came up against Mourinho in the group stages of this season's Champions League - with Real beating the Rossoneri at home and drawing at the San Siro.
And when quizzed on his rival coaches on television show Le Iene, Allegri was quick to stick the boot into the Portuguese boss, who won two Scudetti, the Coppa Italia and the Champions League with Milan's city rivals Inter.
"Every now and then he is pathetic," Allegri said, when asked about Mourinho. "He continuously repeats the same things and it becomes banal. I think he is very talented but his arrogance hides insecurity."
Mourinho is a figure who undoubtedly polarises opinion, no more so than after his recent outburst against Barcelona in the aftermath of Real's Champions League semi-final first-leg defeat to the Catalans.
He was given a five-match ban by UEFA for claiming that Barca received favourable treatment but was widely criticised for his claims, with former Real boss Guus Hiddink insisting earlier this month that he should apologise for his actions.