The Asian side finished bottom of Group H having collected their only point of the tournament in a 1-1 draw with Russia in their opening game in Cuiaba.
Hong was initially persuaded by Korean Football Association president Chung Mong-gyu to stay on as coach of the Taeguk Warriors, but the 45-year-old has had a change of heart and has decided to resign, admitting that he does not think he is good enough to lead them at the 2015 Asian Cup.
He told reporters at a press conference in Seoul on Thursday: "When we left for the World Cup, I said we would give hope to people, but we ended up giving them disappointment.
"A lot has happened over the past year, and I've made my share of mistakes. I made decisions that I felt were the right ones at the time, but as the results show, I've had many failures. I'd like to apologise to fans for letting them down.
"After returning home, I carefully thought about my abilities as a coach and decided I still had many deficiencies. I didn't feel I was a good enough a coach to take the country through the Asian Cup."
Former defender Hong is the most-capped international in South Korea history with 135 appearances.