Veteran captain Georgios Karagounis scored the only goal for the Greeks, champions in 2004, and Advocaat was left stunned as his side, who so impressively beat the Czech Republic in their first match, went from early Group A pace-setters to slumping out of the tournament
"We played quite well - the other team just defended," said Advocaat. "In the second half, against a team like Greece, with all due respect, it was hard to play against them. But it's not that we didn't play well.
"With the staff we worked very hard to have a good team. We were undefeated for 16 games but we didn't win today. That's football. All compliments to Greece.
"They were leading 1-0 after the first half and they are just masters at doing what they did today. We maybe didn't have the sharpness tonight to get that goal."
A draw would have been enough for the Russians but instead the Greeks, who likewise finished with four points, nipped ahead of them on the head-to-head rule as runners-up behind the Czechs.
"After we conceded the goal we had 45 minutes to make it right. But it just didn't work today. It's hard to say why," reflected Advocaat, whose side's finishing was poor.
"You do need a sharpness in front of goal. We had two or three strikers up front, but it just didn't work tonight.
"Even though we lost today, we played brilliantly in the first half. Then they got a goal, and it was a totally different story.
"If you don't score goals and your opponent does, then you lose. You have to score goals. That's what we did in the first game and despite possession, we didn't do that today," concluded Advocaat.