The ex-Juve man was dismissed in the 83rd minute after picking up a second booking for dissent having been cautioned moments earlier for a foul on Medhi Benatia.
Team-mates, both current and former, moved to console the forward, who took a lengthy period of time to leave the field in his outrage.
The sending off compounded a miserable evening for the Argentina striker, who had previously missed the opportunity to level proceedings when his low penalty was saved by Wojciech Szczesny.
In an Instagram post shared on Monday morning Higuain said: “I want to apologise to everyone for my behaviour in yesterday's sending off - the team, society, fans who despite yesterday showed me their love all the time.
“We are people too and we have feelings but I am responsible and I hope it does not happen again.”
Voglio chiedere scusa a tutti per il comportamento avuto ieri in campo, ai miei compagni alla società , ai tifosi che da ieri mi stanno dimostrando ancor di più il loro affetto. Mi faccio carico delle mie responsabilità e farò il possibile perchè non ricapiti. ❤️❤️❤️ #grazieatuttiperilsostegno 👏👏👏 Quiero pedir disculpas a todos por el comportamiento de ayer de la expulsion , al equipo, a la sociedad , a los hinchas que a pesar de lo ayer me demuestran su cariño todo el tiempo. Somos personas tambien y tenemos sentimientos pero me hago responsable y espero que no vuelva a suceder. Algunos lo entenderan otros no . Igualmente pido disculpas a todos. Que tengan una linda vida.
He added: “Some will understand it, others will not. I also apologise to all.”
Higuain joined Milan from the Bianconeri over the summer in a loan deal that will become permanent at the end of the season. Despite two successful seasons in Turin, the forward never truly recaptured the form that saw him score 36 in 35 league matches during his 2015-16 campaign with Napoli.
Higuain’s departure facilitated Juve’s summer signing of Cristiano Ronaldo from Real Madrid, with the Portuguese captain on target for the eighth time in 12 league matches in Sunday’s clash to help ensure his new side maintained their unbeaten start to the Serie A season.
By contrast, Higuain, who himself has five goals in 10 league appearances this campaign, endured a torrid evening at the San Siro. He has now missed five of the 17 penalties he has taken during his time in Italy.
The result sees AC Milan slip to fifth in the Serie A table, while visitors Juventus have opened up a six point lead over second-placed Napoli in their pursuit of an eighth consecutive Scudetto title.