Rumblings over Allardyce's role at Upton Park have persisted amid protests from some supporters in recent weeks and he is expected to deal with the issue at an end-of-season meeting with the club's owners on Tuesday.
Speaking after West Ham's 2-0 defeat at Manchester City that saw the home side secure the league title, Allardyce said: "If you are a manager, this is the highest level in the world.
"I have competed at this level for many, many years. There's only Arsene Wenger has competed at this level longer than me.
"I know how to manage in this league and I know how to turn teams into better teams than when you first take them over, so there you go.
"I find the game strange. I think the volatility of this year's game has been spread across the board by the amount of sackings of managers throughout the Barclays Premier League.
"I think 10 have been changed already and I don't think it has ever been 50 per cent in one season, and if another goes, who knows, it will be more than 50 per cent.
"It's not a very secure industry but it's one we all love and enjoy doing.
"We have had no real threat of relegation for a while and we have done the job after our difficulties in December and January.
"We have won seven of 15, nearly a 50 per cent win rate and we have 14 clean sheets.
"The lads have withstood the pressure and we are established in the Premier League for the second season on the trot, exactly where I was asked to get us to be. Statistically, year three is better but that depends if you can improve your squad."
Allardyce added that City deserved to be champions, as goals from Samir Nasri and Vincent Kompany secured the title.
He said: "They are head and shoulders above the rest because they are top of the Premier League and because they have the best squad.
"They have competed in all four competitions to the maximum level. To win a double - the Capital One Cup and the Barclays Premier League - one has to say they are the best squad and the best team in the league at this moment.
"Liverpool came on a fantastic run but they had no FA Cup, no Capital One Cup and no Europe."