Higuain told Gazzetta dello Sport in an interview published yesterday that he felt something was amiss when he was left on the bench for the Coppa Italia final against AC Milan in May.
"That day, I had the feeling inside me that maybe something had broken down".
Champions Juve had won their opening eight Serie A games and two Champions League fixtures.
Still, he insisted there were no hard feelings.More news: 'Tacky' painting of Trump drinking with other presidents hangs in White House
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"He's very calm and working well, and I'm not the one to respond to things that don't concern me because they are personal", Allegri said at a news conference on Friday, as quoted by ESPN.
"My teammates and the fans treated me really well, but I never asked to leave".
"It wasn't my decision to leave".
Former Napoli striker went on to stress that he gave everything for Juventus winning several titles with the Serie A giants. "I don't see how they could lose the Scudetto without self-destructing". At Milan I immediately had a great love and so they convinced me. "The best solution was Milan".
Higuain - who will take part in his first derby against city rivals Inter Milan on Sunday - has scored four goals for Milan to bring his tally to 115 since his arrival in Serie A in 2013 from Real Madrid. "I found what I was looking for".