The Blues confirmed on Tuesday evening that the tall forward has been granted a work permit ahead of a switch to Goodison Park, and Allardyce was not happy about the developments.
"Every time we go to sign someone, someone else comes in and f****** takes them," the Daily Mail quotes Allardyce as saying.
"If you give me all [of West Ham's injured players] fit from as quickly as possible until the end of the season, I think we'll come out of this.
"Forty [points] is the safe zone over more than 10 years now. It's got to be 22 points minimum for me in the last 16 [games]."
West Ham were beaten 3-0 by Manchester City on Tuesday.