De Boer was shown the Selhurst Park exit 77 days into a three-year contract following a run of four successive league defeats without scoring a goal to begin his tenure.
Palace acted fast by turning to experienced boss Hodgson, who has been out of work for the past 15 months since quitting England, but the 70-year-old says that he feels pity for the man he is taking over from in South London.
"As a football manager and coach, you always have sympathy for people who have lost their jobs," talkSPORT quotes him as saying. "It's always 'there but for the grace go I'. Unfortunately it's fact of life and if a person loses their job and the club turns to you, you accept it of course but you don't accept it without feeling some sort of empathy and sympathy for the person who has gone before you.
"I think that if you say you want to get back but only in the Premier League, then you are just looking for dead men's shoes as well, which isn't a very pleasant situation.Most get the job because some poor devil has lost two in a row, perhaps through no fault of his own. Then you're thrown in to get them to win two or three games in a row.
"In my opinion, football and coaching does not work like that. It's a longer-term process and a process that comes about through your interaction with players that you are working with. At the end of the day, coaches have a certain importance but they will never have the importance of players.
"It is the players that you pay to watch and the players that win the games. All you can do is try to get the best performances out of the ones that you've got. If the ones you have got are not good enough to do the job, unfortunately you will be struggling. It is one of those truisms."
Hodgson, who becomes the oldest manager to have been appointed by an English top-flight club, has previously taken charge of Blackburn Rovers, Liverpool, Fulham and West Bromwich Albion in the Premier League.