Hodgson, who has managed Liverpool, West Bromwich Albion and Fulham in the Premier League, took on his current job at Selhurst Park following the departure of Frank de Boer, who left the club in 19th place and without a league goal after four games.
Seventy-year-old Hodgson has guided Palace to 14th position in the table and the Eagles have lost just once in 11 outings.
"Just because I don't boast of my achievements, it doesn't mean I have ever thought anything other than I am a very good football manager," Hodgson told Sky Sports News. "Whether Palace win or lose, at the end of my time at Crystal Palace, I will still be thinking 'I am a very good football manager'.
"I know it, I see it every day. I've been working for 41 years: I've got so many titles. I've been manager of the year, I've got goodness knows how many manager of the month awards. I've had 100-odd games for national teams and 150 in European competitions.
"I don't think that after leaving England I was absolutely ready to turn my back on [management]. After England, I didn't think I've got something to prove. I was bitterly disappointed that we lost a vital game but I have a totally different attitude."
Hodgson's Palace, who remain just two points outside the relegation zone, meet local rivals Brighton & Hove Albion in the FA Cup on Monday evening.