Bilic, however, insisted his squad - now sixth in the league - are focused only on their performances, rather than feeling hard done by referees.
"On one hand, it's nice to know that we could be second in the table (with the correct decisions) but the most important thing is we are playing well and we are in a good position going into the last four games," he told reporters on Thursday.
"I don't want to talk about it anymore now. Do good decisions and bad decisions even themselves out? Well, according to the table, they don't!"
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Adding to the remarks by former World Cup assistant referee Turner, another former top-flight referee, Keith Hackett, said the intimidating atmosphere at Upton Park could be pressuring referees into making the wrong calls.
"I think what might come into play is the fact that it's a pretty vociferous crowd. West Ham followers make the referee at times feel uncomfortable by the very nature of their reaction to decisions, right or wrong," Hackett told British media.
Bilic has played down speculation linking Aaron Cresswell with a move away from West Ham United, after the left back's promising form this season caught the eye of a number of clubs.
Cresswell, 26, joined the London side from second tier team Ipswich Town in 2014 and his two goals and four assists saw him voted the club's player of the year during his debut campaign.
Cresswell has enjoyed another fine season and played a key role in West Ham's unexpected charge for the European spots in the league.
"Aaron is having a great season... He is almost a play maker from defence. Aaron improved defensively and is almost a complete player now," Bilic said. "He naturally became of interest to so many good clubs. I spoke to him. First, he is under contract and second, and more importantly, he is really happy here and can't wait for the future."
West Ham travel to face 13th-placed West Bromwich Albion at the Hawthorns on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Mark Heinrich)
