Hiddink's last game in charge of the co-hosts ended in disappointment as they went down 3-2 in Daegu.
"I would have liked to get third place - desperately. But we made some big mistakes in the first half in defence," he admitted.
"But when I see and hear the public reacting to the team and what they did in the second half, I can be very proud in general of these guys."
There was tremendous support from the fans all over the country
Hiddink has been linked with a return to his former club PSV Eindhoven now his mission with Korea is over.
"I don't know what the future brings but I like to be on the pitch every day with players," he said.
"That's why I am considering my future. Nothing is definite or settled yet.
"I have worked very hard in 18 months to try to get the players very competitive.
"Thanks to the Korean public. I think there have been some changes in the way we act in the team and reflected by a lot of people outside the team and I would like to thank them very much.
"There was tremendous support from the fans not just here but all over the country.
"I'm very happy to be here and I'm very happy to have worked here."
Midfielder Lee Young-Pyo said the Korean players would do their best to ensure their World Cup display did not turn out to be a one-off.
"It would have been regrettable if it had been our last chance, but I'm sure there will be more such chances in the future," he insisted.
"I hope this World Cup will be a stepping stone for Korean football."