West Ham have made an awful start to the campaign, and they are currently stuck down in 16th place in the Premier League table.
The pressure has been ramped up on Bilic, after the Hammers went out of the EFL Cup following a 4-1 loss to Manchester United yesterday.
Bilic was heavily criticised for naming a number of fringe players in his West Ham starting line-up at Old Trafford.
However, Nolan insists that West Ham should stick by Bilic - as he has had to deal with a lot of complications this season.
“It’d be very unfair,” Nolan said, when asked whether Bilic should lose his job at West Ham.
“Slaven did a fantastic job last year, and they haven’t had a great start but a lot of things have changed off the field. You have to give him time to embed those people and get used to the new stadium. It’s all different and it’s difficult.
“Everyone should realise how difficult it is moving from the Boleyn to the Olympic Stadium.”
West Ham’s next match comes against Arsenal in the Premier League at the London Stadium.
If the Hammers can pick up a victory over their London rivals, they could move up to as high as 12th in the top flight standings, and that would relieve some of the pressure building on Bilic’s job.