Friend awarded the Tigers a penalty early in the first half when Robbie Brady went down inside the box.
However, Allardyce insists that it was the wrong decision and accused Brady of simulation.
"It wasn't a penalty. Robbie Brady profited by simulation - by diving. Referees are supposed to be good at spotting these things, but [Kevin Friend] wasn't," BBC Sport quotes him as saying.
The Hammers boss also believes that his side should have had a penalty of their own and says that he will make his feelings known to Friend.
"Then Jake Livermore's handball wasn't given, so that's two big decisions that have gone against us. The referee has given a very poor performance today. I will go and mention to him now that I am disappointed," he added.
West Ham are now 16th in the Premier League table.