Allardyce never won the fans over during his time at Upton Park, and things came to a head in the 2014/15 campaign.
West Ham made a hugely impressive start, but they fell away over the second half of the campaign and found themselves tumbling down the table.
And Bilic believes that the Hammers’ loss of form could not have been attributed to just one issue, as Allardyce would have rectified things had there been a simple solution.
“I know what happened last year when West Ham were in the top four at Christmas and then fell away,” he said.
“They had a few injuries and the squad was very tiny last year. I watched a lot of the games and in the first half of the season West Ham were a little bit lucky in some of the games, in the second half we were more unlucky. But maybe the players went into a safe zone and that can be very dangerous.
"That can happen to you in any job — it is nice to be relaxed and comfortable but you can get into a comfort zone where you drop your level.
“Once you lose that five per cent of overdrive, it can have a major impact. You can’t see it straight away and once it is gone, it is gone. It wasn’t one thing that happened last year because if it was Sam Allardyce would have changed it because he is a great manager.”
Bilic will be hoping that West Ham’s season does not follow a similar path this term, as they have made another encouraging start.
The Hammers have climbed into third spot in the Premier League table, and they are the second top scorers in England’s top-flight.
However, even if West Ham do have a dip in form, Bilic shouldn’t face a backlash quite like Allardyce did from the supporters – as he already appears to have united all of the club’s followers behind him.