The former international defender has criticised the pair for allegedly clashing when the Rossoneri boss went to visit the club's youth camp last week
Allegri reportedly turned up at the Vismara Centre, which is where the club’s youth teams play, to watch training. Inzaghi, the current manager of Milan’s youth team, allegedly accused his former boss of not taking his job seriously, which resulted in a heated argument between the two.
The Montreal Impact defender believes that attempts to cover up any rift are failing, and he thinks the two have acted in a childish manner.
"Their argument? It's the behaviour of children," the 36-year-old said to Sky Sport Italia.
"If it went as I read, it was childish from both of them."
The centre-back then discussed the Rossoneri's current struggles that have seen them manage just one win in their first five games.
"It is not the first time the team has been in trouble, but in the past we were able to finish the season well. Allegri is being doubted, but I do not understand who could be the alternative."
Finally, Nesta was full of praise for current Roma boss Zdenek Zeman: "He is a great coach, every player should expect to be coached by him because he's the best to teach football."