The 59-year-old will lead the Hammers into a Capital One Cup semi-final first leg at Manchester City on Wednesday with a big night for the club overshadowed by their poor league form.
Sitting 19th in the Barclays Premier League and on the back of a 5-0 FA Cup defeat at Nottingham Forest, many would have been taken aback by West Ham's co-chairmen David Sullivan and David Gold's public support for Allardyce on Monday.
But Allardyce knows it is true to form for the duo, who were renowned for giving their managers a chance during their spell at Birmingham.
"Their track record proves they haven't been too rushed into anything," Allardyce said.
"They've never been too rushed into what decisions they make. Over the last 18-20 years, the managers they've had, they've given them a good chance and stuck by them when things are not going so well."
But, with six top-flight bosses already sacked so far this campaign, Allardyce is also aware he is in a different position to many of his peers.
"On today's stats you just have to look at them, look at this season alone," he added.
"The reactions are getting quicker and quicker and quicker due to the impatience throughout the game for success. Success isn't built overnight.
"Success has to be built over a sustained period of time. There are difficulties within that time that you experience and you have to try and get through, and history tells you continually changing managers doesn't mean success.
"I'm realistic to know I have to get results, particularly quickly from my point of view, as a manager."
Hammers' midfielder Matt Taylor has also praised Sullivan and Gold for giving Allardyce time to turn things around.
"For me it shows the people in charge of this football club are prepared to put their neck out and back the manager and quite rightly so," said the 32-year-old.
"It shows also that there is quite a good air of stability about the football club in terms of coming right form the top.
"There wasn't any need to do it [publicly back Allardyce], they obviously wanted to do it and I think it was the right thing to do. Hopefully players on the pitch can help the manager along and start picking up some results."