The 59-year-old has guided West Ham to just three wins so far in the Barclays Premier League and has seen the three clubs who sit below his 17th-placed side all change managers since the start of the season.
Bottom club Sunderland are the visitors to Upton Park on Saturday with Allardyce firmly focused on turning things around on the pitch rather than think if his job could soon come under threat if co-chairmen David Sullivan and David Gold feel a change is needed.
"I don't think about what the owners will or might not do," he said.
"It distracts me from my job and I think that my job is achieve the best possible results for West Ham and if I don't do that you get sacked and if you do do that, you don't. It's that simple in my job.
"They cannot be patient forever if I continue to lose football matches. It's impossible for them to ride the pressure that will come upon them, impossible not to succumb to that pressure like many other owners have done."
West Ham were nine points better off at this stage last season after an impressive start to the campaign for the side who had returned to the Premier League through the play-offs.
A more difficult start this time around has left the Hammers further down the table but with Allardyce feeling a run of form is just around the corner.
"I told the players how important that start was," he added.
"If you don't get that start the pressure comes on you straight away. That's exactly what we've got now so we've got to believe that we will have an eight-game spell where we get over 14 points which is what we plan throughout the season in eight-game phases so we're in apposition where we've got to try and do that.
"We never talked about relegation last year and never did we get threatened with any relegation problems because we were never lower than 14th."
Defeat on Saturday could see West Ham drop as low as 19th and then the pressure would be on Allardyce with clashes against Manchester United and Arsenal on the horizon.