Despite having netted 55 goals over two seasons at Juventus, the Argentine saw the exit door opened in Turin over the summer.
The Bianconeri’s capture of Cristiano Ronaldo saw the South American deemed disposable, with various landing spots mooted.
Chelsea were among those to be credited with holding an interest, with Sarri having worked with Higuain in a previous post at Napoli.
He was, however, to be left empty-handed, with the Italian telling Sky Sport Italia: “Higuain? It's a little regret but in the end everyone after the market has a few little regrets.”
The 30-year-old frontman admitted during his official unveiling at San Siro that he did not feel wanted enough at Chelsea to make a move to England.
He said: “I have huge respect for Sarri, but he was the only one who wanted me at Chelsea.
“Here at Milan everyone wanted me.
“The motivation and conviction they showed at Milan was fundamental.”
While the Blues missed out on one attacking target, Sarri was able to bolster his midfield and goalkeeping ranks during the Premier League transfer window.
Jorginho was brought with him from Napoli, Mateo Kovacic arrived on loan from Real Madrid and Kepa Arrizabalaga became the world’s most expensive shot-stopper.
Sarri said of that business: “The club was willing and we took a great goalkeeper, very young but he can become a great goalkeeper.
“For the rest, Kovacic is a player who can be big, Jorginho has arrived, the backbone is already there.”
Kepa and Jorginho made their respective debuts for Chelsea in a Premier League opener with Huddersfield on Saturday, with the former keeping a clean sheet and the latter converting a penalty in a comfortable 3-0 win.