The 64-year-old, who oversaw his last game at the helm of the national team, lamented his side's 'unfortunate' loss on Saturday
The Russians, semi-finalists in 2008, began the day in top spot, only needing a draw against the Ethniki to advance to the last eight.
However, they were lethargic at the National Stadium in Warsaw, and were made to pay when Giorgos Karagounis struck in the second minute of added time at the end of the first half to secure progression.
Advocaat, who is set to take the reins at PSV, believes his side deserved better before offering his thoughts on the failed campaign.
“We can look at everything negatively, but we played well against the Czech Republic and Poland, we played well today,” he told NOS.
“We totally outclassed Greece. We gave away the first goal and didn't recuperate from that blow. They are masters at bleeding a match to death.
"I'm not really too interested in what others say about me. My staff worked really hard, we were undefeated for 16 matches.
"We were unfortunate. We should have won today but that's football so compliments to Greece."