Ten years on from their unexpected triumph at the 2004 European Championship, Greece head to the World Cup as one of the lesser-fancied teams, despite their FIFA ranking of 12th.
Fernando Santos' men have been drawn in Group C alongside Japan, Ivory Coast and Colombia, with the latter representing Greece's first opposition in Belo Horizonte on Saturday.
Karagounis is perfectly happy for others to underestimate his side, insisting they will punish any complacency.
The 37-year-old Greece captain told FIFA.com: "Sometimes it's good because whether or not they praise or respect you, the truth is on the pitch. For the last 10 years, this is where we have answered our critics.
"I think whoever doesn't respect us will pay for it. It's best not to cross us.
"We know who we are and what we can do. If we stay together as a team, we can achieve big things."
Coach Santos is approaching four years in charge of the national team after taking over from Otto Rehhagel – the tactician behind Greece's Euro 2004 success – in July 2010 and Karagounis is confident the Portuguese can guide the team out of the group.
He continued: "He's (Santos) been our coach for four years now. We know him and he knows us, so there are no surprises.
"Under him, we reached the quarter-final of the EURO in 2012 and that was a great achievement, to be one of the best eight teams in Europe.
"Now we are here at the World Cup again under his guidance.
"He has built on the lessons of our previous coach and with his knowledge of the team and our knowledge of his philosophy, I am hopeful we will get to the second round."
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