The Egyptian defender was sent out on loan to Saudi Arabian outfit Al-Ittihad, who will make the deal permanent at the end of the season.
And Bilic has confirmed earlier reports that he had assurances from the club that Hegazy would not be sold.
"He has experience. He is a top professional," Bilic told BBC Sport.
"I wanted him to stay and he wanted to stay and then something happened and then he is off although I had assurances from the club that he would stay.
"That happened yesterday. Of course I am not pleased. I am really disappointed because we need players. There is of course the economic side but we are a football club."