Since penning a season-long loan deal at the London Stadium, Hart has conceded 13 goals in seven Premier League fixtures, which has led to criticism of the Manchester City and England stopper.
However, Bilic has moved to defend Hart by suggesting that the 30-year-old has become an "easy target" for both the media and supporters.
The Croatian is quoted by Sky Sports News as saying: "I think you don't appreciate him. 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."
Hart has kept clean sheets in three of his last four outings in the top flight.