Inzaghi only took charge of the San Siro side last summer but was fired at the end of disappointing 2014-15 campaign which saw the Rossoneri fail to qualify for Europe after finishing 10th in the Serie A standings.
Sinisa Mihajlovic, who stepped down as Sampdoria coach on June 1, is now expected to fill the void and while El Shaarawy has the utmost respect for the Serb, he remains disappointed by Inzaghi's dismissal.
"I think that he gave all of himself for the Milan shirt, so I'm very sorry to see him sacked because I know very well the passion that he put into the job," the 22-year-old striker told reporters on Wednesday.
"Mihajlovic? He's a great coach who has done very well but it's not yet official so I can say no more."
However, El Shaarawy did admit that he hopes no matter who is charge next season is given plenty to spend in the transfer market.
Indeed, there is speculation that Milan owner Silvio Berlusconi is willing to splash up to €150 million on new players this summer and the Rossoneri have made former striker Zlatan Ibrahimovic one of their primary targets.
El Shaarawy was reluctant to be drawn on the Swede's possible return to the Giuseppe Meazza but he was more than happy to reiterate his commitment to the club.
"For now they are only rumours, but regardless of Ibra, I hope that Milan can have a big transfer market and can again be competitive, both in Italy and in Europe," the Italy international added.
"I have a contract with Milan. I hope to stay and return to being great with Milan."
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