The shock result had many pundits and fans tipping the east Londoners for big things this season with Bilic's new emphasis on attacking football.
The performance improved drastically in the second half and Bilic's side pulled one back through star man Dimitri Payet.
The damage had already been done, though, and the Hammers were brought crashing back down to earth after the euphoria of the Arsenal result.
'A common problem'
Now in the wake of the defeat to Ranieri's men, Bilic has defended his players and told West Ham's official website that the club's fans are used to beating top sides and then going on to lose the next game.
“We are not going to panic, we knew what we had before the game," Bilic told www.whufc.com.
"For West Ham it is not that uncommon to beat Arsenal and then lose the next match.
“In football, you have many results like Saturday’s where, somehow, clubs find it easier to play away games.
"They are not under the same pressure to win or to play well. On the other hand you have to use your home crowd to make it easier for you."
Bizarre statement shows Bilic understands the club
While it may seem a bizarre thing to say after a defeat from which supporters are still smarting, it shows Bilic is aware of the challenge that faces him.
Any true Hammers fan will testify that the club has made a habit over the years of beating a top side before losing to a supposedly inferior team next time out.
In fact it is a trait that is often used against the club by rival fans claiming that is the real 'West Ham way'.
What it does show, though, is that Bilic knows the club inside out and will not try to hide away or make excuses and his honesty will go a long way with the club's loyal and knowledgeable fans.
The former Croatia boss will also know the best way to fix the problem, go out and beat Bournemouth next week to get everyone back on the positive train.