Onana has completed a move to Manchester United for a fee of €51m and another €4m in add-ons from Inter.
The 27-year-old has signed a five-year contract with the Red Devils and has joined the Manchester United squad in the US for their pre-season tour.
Inter needed to sell one of their top performers this summer and ultimately decided to sacrifice Onana to bring in money for their coffers.
But according to Italian broadcaster Sportitalia, Inzaghi was not on the same page when it came to the club’s decision to sell the goalkeeper.
The Inter coach was not in favour of letting the Cameroonian goalkeeper go in the ongoing transfer window.
Onana was a pivotal player for the Inter coach in the way he set up his team, especially their defence.
Inzaghi was not interested in losing him but Inter had to cash in once Manchester United agreed to pay a big fee for a player they signed for nothing last summer.
The Nerazzurri are yet to bring in someone to replace Onana and Inzaghi is without a senior goalkeeper in his squad at the moment.