"On the decisions -- and Adrian's red card in particular -- I won't criticise the referee," Bilic wrote in his column for the London Evening Standard.
However the manager added that he was "shocked" that the offence carried an automatic three-match suspension.
"When I heard the ban I couldn't believe it for a whole day ... It should be one match, maximum," Bilic wrote.
"The rule is the problem. Adrian's offence did not warrant that ban but the FA had to enforce it.
"My opinion is that every red card should be looked at objectively and individually," the 46-year-old Bilic added.
"Adrian's absence for that many games is a big blow for us and definitely we didn't deserve that.
"It's a very important issue."
The manager also said his side were very disappointed to lose to Leicester City in their second game of the season after winning away at Arsenal in their Premier League opener.
"I don't like to look for excuses. We were beaten because of our performance in the first half," Bilic said.
"When you are two goals down in the Premier League it is very difficult to recover -- maybe once in 10 games you can do that but it's very hard," he added.
"We did well for the first 10 minutes but I was very disappointed with the rest of the first half.
"We had a good reaction in the second half but, basically, there is no reason why we shouldn't be doing that from the start -- especially at home in front of our own fans."
(This story fixes club name in headline.)
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
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