On Monday, Palace announced that Allardyce's replacement De Boer had been removed from his position after losing each of his opening four league games at the club without scoring a goal.
The decision comes after Palace were unfortunate not to gain a positive result at Burnley on Sunday afternoon, but Allardyce has indicated that the call to sack De Boer should come as little surprise given the money now circulating in English football.
Allardyce told Sky Sports News: "I have just heard the news that Frank has left today which is obviously very disappointing for him and for Palace, but it shows the panic in football today is ever increasing due to the size of the money and the fear of losing your position in the Premier League.
"As a manager, you have to live or die by your results and unfortunately now that is quicker than ever. It is a great shame that Palace have not continued where I left off.
"I watched them yesterday and I have to say the fact they actually lost the game was beyond me. Twenty-two attempts at goal, complete domination but unfortunately the guys at the end, when the chances came, couldn't put the ball in the net."