The players, Son assured the fans, would not allow the result - which eliminated 2014 FIFA World Cup winners Germany - to make them complacent.
"I am sorry to our fans that we didn't live up to our promise of reaching the knockout stage," Son said. "But I think we all saw some hope from the win over Germany.
"However, the win over Germany doesn't mean we are satisfied. We will continue to work hard," said the Tottenham Hotspur forward.
Korea Republic's next major tournament is the AFC Asian Cup 2019 which the East Asians are targeting to win, as the last of their two titles came in 1960.
The win over Germany, said Son, was just the boost Korea Republic needed as they set their sights on the AFC Asian Cup UAE 2019.
"Defeating Germany will be a lasting memory from the 2018 World Cup," said Son, who scored the team's second goal after a lung-busting run which saw him slotting into an empty net six minutes into added time.
That confirmed a first ever win for an Asian team over the reigning World Cup winners in an official match.
Although Korea Republic failed to advance to the Round of 16, the performance against Germany came at a time the team were desperate after having suffered defeats to Sweden (1-0) and Mexico (2-1) in Group F and has lifted spirits ahead of the AFC Asian Cup UAE 2019.
Korea Republic are in Group C along with China PR, Kyrgyz Republic and Philippines in the January 5-February 1 AFC Asian Cup UAE 2019.
Sources: Yonhap, FIFA via Getty Images