Instead, Karagounis was booked for diving, much to his dismay as coach Fernando Santos held his hands to his head on the touchline.
Greece defender Giorgos Tzavellas crashed a free kick against the angle of post and upright in a rare Greek attack in the second half.
Russian fans had poured into the Polish capital during the day and heavily outnumbered their Greek counterparts, turning Warsaw's National Stadium, which was nearly full to capacity, almost into a 'home' venue for Dick Advocaat's side.
There were no reports of a repeat of the street violence that marred the build-up to Russia's clash with Poland on Tuesday.
Image: Greece's Giorgos Karagounis, center, appeals for a penalty during the Euro 2012 soccer championship Group A match between Greece and Russia in Warsaw, Poland, Saturday, June 16, 2012.