Co-chairmen David Gold and David Sullivan faced calls from frustrated supporters from midway through 2013-14 for a change of management as results and performances failed to meet their expectations.
A 5-0 FA Cup defeat at Nottingham Forest followed three days later by a 6-0 League Cup semi-final first-leg hammering at Manchester City in January represented a nadir in Allardyce's tenure, which has included promotion back to the top flight.
However, Gold and Sullivan kept faith with Allardyce under the proviso that West Ham target a top-10 finish and play more attractive football.
The 60-year-old has spent wisely – striker Diafra Sakho has been a revelation with five goals in six league games - and West Ham head to a Premier League clash with champions City on Saturday fourth in the table.
And Allardyce is thankful that his strong relationship with Gold and Sullivan has led to such a turnaround in fortunes.
"They are the best owners I've ever had," Allardyce told the Daily Telegraph.
"They are loyal.
"They could have cracked under pressure. At one stage I thought it might have been very, very close in December and January [to being sacked].
"It's very difficult to take the pressure when you're the owner and every man and his dog is saying, 'You've got to get rid of him'.
"They were saying it to them through social media, through abusive messages and emails. The owners are very easily contactable [Gold is active on Twitter] – personally, I'd say too easily. They get affected by it.
"I've no problem with that. My life's about adjusting to owners' needs.
"Everyone wants to have the best team, and play the best football, but that takes some building, some doing."