Hong's men went into Thursday's final Group H clash needing to beat Belgium comfortably and hope that Algeria dropped points against Russia.
Fabio Capello's side held Algeria to a 1-1 draw, but in Sao Paulo Korea ultimately lost 1-0 to 10-man Belgium, who had Steven Defour dismissed just before the break.
The defeat sees Korea finish bottom of the group with a single point, which was picked up in their opener against Russia, and Hong - who appears to be considering his future after just a year in the job - conceded that they failed due to him.
"I'm sorry if this has put a damper on your morale," he said.
"It's difficult to give a grade to my players. There were a lot of trials and errors.
"I think our players did their best during the whole process. It's difficult to self-evaluate but it was my shortcomings as a coach that caused this result.
"I will decide later on whether I will stay in the job.
"We played quite well and there were chances where we could have counter-attacked. When the Belgian player (Defour) got the red card the situation changed and I think we concentrated too much on the centre."
