The 35-year-old put his country ahead seconds before the end of the first half of their crunch match with hot favourites Russia on Saturday, sending their fans wild both in Warsaw's National Stadium and back in their crisis-ravaged homeland.
"When the team left Greece, we all said with one voice that we will give our all. And we'd give our all in any event, let alone now, when our compatriots aren't having the best time," said Karagounis.
"I believe that this has put a smile on their faces," added the Panathinaikos player, who won his 120th cap to equal the record set in 2007 by Theo Zagorakis, his captain at Euro 2004.
Along with fellow midfielder Kostas Katsouranis and goalkeeper Kostas Chalkias - who missed the Russia game due to a hamstring injury - Karagounis is one of a trio who were in the squad at Euro 2004.
At that tournament, the unheralded Greeks found glory by beating favorites and hosts Portugal in the opening match - when Karagounis scored - and again in the final.
"Today's saga compares with what happened in Portugal. We managed to qualify against all odds. That's why the value of this qualification is great. We managed to overcome huge obstacles," said Karagounis.
However, already carrying a yellow card from the Greeks' 2-1 defeat by the Czech Republic he was booked in the 61st minute for contesting Swedish Jonas Eriksson's refusal to award a penalty when he was brought down in the box.
As a result, he will have to sit out Greece's quarter-final next Friday in the Baltic port of Gdansk, where they look set to face powerhouses Germany if the latter top Group B as expected on Sunday night.
Already annoyed over disallowed goals against the Czechs, Karagounis bemoaned his fate and said his team had been hard done by against Russia too.
"Maybe UEFA has to check the video of the game. This is not fair. All referee calls were against our team," he said.
"That's why I think everyone deserves our congratulations," he added.
Greece's Portuguese coach Fernando Santos is already considering his options for the quarter-final, given that his talismanic captain is set to be out of action.
"If Karagounis can't play in the next match, I am the coach so it's up to me to find a solution," Santos said.
For Karagounis, however, the personal frustration does not detract from the pleasure of seeing Greece reach the knock-out phase of an international tournament for the first time since they won Euro 2004.
Despite their European victory eight years ago, they failed to qualify for the 2006 World Cup, and did not clear the group stage at either Euro 2008 or the 2010 World Cup.
The Greeks' Euro 2012 campaign had begun with a 1-1 draw with Poland - the tourmanent's co-hosts along with neighbours Ukraine - where they showed their fighting spirit by battling back with 10 men to equalise.
They would have won but for Karagounis having a penalty saved.
Their 2-1 defeat by the Czechs meant the Russia match was a must-win.
"We played for one result," Karagounis said.
Santos, who has said he sometimes feels more Greek than the Greeks themselves, underlined the sense of pride at advancing at football's Euros while the country is stricken by the euro currency crisis.
"Everyone has to respect Greece because of its history and the principles of democracy, science," said the coach, who took over in 2010, succeeding German Otto Rehhagel who during a decade in charge steered Greece to the title at Euro 2004.
"What inspires us is the history of Greece. This is the thing that inspires me the most because the Greek people have huge pride for their tradition and history and I think respect from everyone is well deserved."