Five of the Barclays Premier League's bottom six teams have changed managers this term, with basement club Fulham swinging the axe twice.
But Upton Park co-chairmen David Sullivan and David Gold stuck with Allardyce and have been rewarded for their patience with 10 points from the last four games, lifting the Hammers out of the bottom three and up to 11th.
West Ham host Southampton on Saturday looking to make it four wins on the trot, but Allardyce knows the owners' patience will only be vindicated by where they finish.
"We'll only know that at the end of the season, when we have achieved what we want to achieve and that is to finish as high up the table as we can," he said.
"We are not out of the woods yet but we have made great strides, all of us, including the co-chairmen and vice-chairman Karren Brady for getting some new players in January.
"Everyone has played a part to alleviate the situation we were in and it's my job to make sure that pays off. At the moment it's going well but Southampton are back in good form again so it will be a difficult game.
"But hopefully with the form we are in we will be big enough and strong enough to conquer them."
West Ham's recent run has been built around a rock-solid defence - dubbed 'Adrian's Wall' after their Spanish goalkeeper - who have conceded just one goal in six league matches.
In fact their 13 clean sheets this season is the best defensive record in the Premier League.
"It's nice to be top of one league for a change," added Allardyce.
"But the basis for any winning side is you have to be a sound, solid defensive unit no matter how many talented players you have.
"That's the basis to start your success on, irrespective of what any other manager might portray publicly, privately they will say the same. It's just that I am brave enough to say it."
Allardyce is still without striker Andy Carroll, who completes his three-match ban for his controversial red card against Swansea earlier this month, so the Upton Park boss is set to stick with the side which secured back-to-back 2-0 wins over Aston Villa and Norwich.