Calls for the 30-year-old to be dropped as England's number one goalkeeper has grown louder and louder in recent times.
But Bilic disagrees and says Hart's recent performances for the Three Lions have been outstanding.
"I think you don't appreciate him," the Hammers manager said. "I watched the game against Slovenia and he was man of the match.
"Has he become an easy target? Yes. The guy is brilliant. I'm not just talking about goalkeeping now, the guy never slaughters anyone in the job, he is taking the bullets, he is there every single time whether he is at City or Torino or West Ham.
"He is a great professional and very interested in the squad. He is a top pro."