The 70-year-old has been out of work since stepping down from his position with the Three Lions in June 2016, fresh on the back of a humiliating last-16 defeat to Iceland at the European Championships.
Palace have turned to Hodgson to replace Frank de Boer, who was given his marching orders on Monday following a disastrous start to the campaign, and the experienced Englishman is now looking forward to the next chapter in his career.
"It is not for me to say whether I or other managers have got a point to prove. I am not a great believer in points to prove I must say," he told talkSPORT. "The fact is that all jobs end in a way that you don't want them to end.
"Tournament football is tournament football and unfortunately you lose a game in tournament football and it is going to be a bad end because you are out of the tournament. In general terms, I thought the four years, quite satisfied with the work we did. Fifty six games and seven defeats and a lot of very good results and performances during qualifying matches.
"Unfortunately in the tournaments we were not able to carry that through but I am hoping that in this current group of players, many of whom we brought into the team and worked with, will be the ones who lead England on in the next tournament. But for me, that is a chapter in my book which has been closed and it has no effect whatsoever on the work that I have ahead of me."
Hodgson was also in charge of England for the 2014 World Cup, exiting the competition after just two group-stage matches.