Victory against Inter Milan on the weekend has the Rossonero sitting second on the Serie A table, two points behind leaders Roma.
On the influence Allegri has had on the club's revival, Capello enthused: : "I'd say 70-80%, because against the big teams you can't win unless you've got into the players' heads.
"Throughout a season, there are stages to overcome, and you only overcome them if you're convinced the coach's instructions are correct.
"Let's also not forget that he doesn't have a very strong squad at his disposal, and therefore doesn't have a wealth of options to vary his tactical plan."
Capello then addressed Allegri's team management, emphasising that it's not just about tactics, but also greater attention to rules and behavior at Milanello.
He stated that, while some might consider these aspects to be minor details, they are actually "the very things that make the difference," as they serve to create a team and a winning mentality, which have always been "the soul and strength of AC Milan."
Capello concluded that, with the way Allegri is handling the situation, he is "bringing the old AC Milan back to life," proving that "Max has a good memory."