Carroll was out injured for much of Allardyce’s time at Upton Park, but when he did return to fitness, the 60-year-old boss was keen to put him back in the first-team straight away.
Bilic, on the other hand, has been far more cautious with Carroll – and the England international says that he is currently working to his own schedule, allowing his body the chance to fully recuperate.
“I’ve been doing my own training, my own schedule,” Carrol said. “I’ve missed a day or two during the week sometimes. He’s understood what I need. He’s been great.
“He’s spoke to me and told me that I don’t need to train every day and to make sure I take a day off.
“I came back from injury last season and then I’d go straight in and that wasn’t the best thing to do, but that’s what I wanted and what the manager [Sam Allardyce] wanted. But Bilic has put a stop on it and he says you can’t do that.”
Carroll has spent much of his time on the sidelines recently, as injuries have plagued his time with the Hammers.
However, he seems to be back to fitness now and will be hoping to avoid any further complications, as he looks to prove his worth.
Carroll made a huge impact in the Hammers' 2-1 victory over Chelsea, as he came off the bench and netted the winner for his side, but his first start of the campaign did not go according to plan.
The England international was picked to lead the line against Watford last weekend, but he was not at his best and one of his errors contributed to his team’s 2-0 defeat.