Son, South Korea's most-capped player and second-highest goalscorer, missed a few chances in a 1-0 defeat by Austria on Tuesday, with his performances under the microscope in the build-up to this year's World Cup.
The 33-year-old began South Korea's 4-0 thrashing by the Ivory Coast last week on the bench, with Hong explaining that was due to illness.
"Son Heung-min is the heart of our team, and I have never once doubted that," Hong told reporters.
"I tried to monitor his minutes because he was battling a cold when he first reported to camp. As far as I am concerned, Son Heung-min has been doing a superb job as captain and one of the veteran players."
Son, who is yet to score for his club Los Angeles FC in the MLS this season, this week hit back at suggestions that there had been a dip in the level of his performances.
"When the time comes for me to leave the national team, then I will do it on my own. If I can no longer play at a high level, then I shouldn't be on the national team," he told reporters.
"Now I have to return to my club and try to perform better. It's disappointing that people talk about decline whenever I hit a dry spell.
"I know there are high expectations on me because I've scored so many goals over the years. I am always doing the best I can, and I am feeling good physically."
South Korea will play in Group A at the June 11 to July 19 World Cup, alongside co-hosts Mexico, South Africa and the Czech Republic.