The Taeguk Warriors were arguably the better side in the final at ANZ Stadium on Saturday, controlling the ball and probing the hosts' backline throughout.
Trailing to Massimo Luongo's long-range strike just before the break, Korea forced extra-time when Son Heung-min sensationally equalised in the 91st minute.
It was not to be for Stielike's valiant troops, substitute James Troisi restoring the Socceroos' lead and breaking Korean hearts in the process.
"I don't agree we're not champions," the German said.
"I agree we don't have the Cup. But with the way we played today, we won many hearts.
"All the messages I have received, everyone is giving a big hand to the players. It could have gone either way. I think the best thing at the end of this game would have been a draw and both teams to take two years each of the Cup."
A decorated player with Borussia Monchengladbach, Real Madrid and West Germany, Stielike has only been in the job since September but already appears to have developed a strong bond with the country and its football, preparing a statement in Korean to read for the media.
"First I will tell you something in Korean because it's coming deep from the heart ... the translation is 'Korea, you can be proud of your boys.' This is what I'm thinking and more what I'm feeling.
"I will tell you a story. Two days ago we did a session with two groups. There were 10 players, eight outfield players, two keepers.
"They played a small game. It means there's a lot of action for the keepers. We only have one player in the whole group who didn't play one minute (of the tournament). This is the third keeper. So I was looking to this game and this guy, the way he was working - if anybody didn't know our team, they would say he was number one."
With team spirit and effort clearly in abundance, Stielike was asked what Korea need to take them to the next level and end their wait for a first Asian Cup title since 1960.
"What we need is with the [development] of the young players in the Korea, we have to work more with the ball.
"The problem in Korea is the way kids are taught, mostly at the schools and universities ... They teach them to win. We have to teach them to play football. This is different."
