Russia's Dutch coach Guus Hiddink claimed his side were better than Holland "in all components of the game".
Hiddink's team bounced back from conceding a late leveller to Ruud van Nistelrooy - the Real Madrid striker forcing extra time by cancelling out Roman Pavlyuchenko's opener - to run out 3-1 winners after extra time through goals from substitute Dmitri Torbinski and man of the match Andrei Arshavin.
Hiddink, who before the match played down fears of being labelled a traitor back home, was understandably delighted with his side's showing.
"I'm extremely proud of the achievement of my team," he said.
"I have not experienced that very much in my career. If you see the game - and I don't know if I am still realistic and without too much emotions to analyse the game well - I think the team was superior in the control, in passing, but also technically and also in physical parts superior to the Dutch team, which is tremendous because I know how they prepare tactically and physically.
"I don't mean it (superior) as an arrogant word, but we were better than the opponents in all components of the game."
Hiddink also admitted he regretted accepting being labelled a traitor in Friday's build-up.
"In my concept, the word 'traitor' is a very bad word," he said. "But let's have it considered a little bit more light.
"Of course, in my position I would have loved to outclass the Dutch team and if we win - an unexpected win - then I'm very happy.
"But the word 'traitor' was not used by me. I don't like the word."
The result is the third time in as many quarter-finals that the pool winner has been knocked out by the team that finished second in their respective group following Portugal's defeat to Germany and Croatia's elimination at the hands of Turkey.
Russia only clinched their place in the last eight with Wednesday's 2-0 victory over Sweden, while the bulk of Marco van Basten's first-choice players had had over a week to recuperate since their stunning win over France with the coach having made nine changes for Tuesday's triumph over Romania.
But it was Hiddink's team who looked the more sprightly in the additional 30 minutes.
He said: "If you look at the preparation after a tough Swedish game and after a tough Greece game - especially after Sweden - we had two days to recover.
"I did not complain a lot, a little bit, about the short preparation time for this very difficult game.
"The short preparation time meant we could hardly work tactically but we did it yesterday and with meetings we have with team in the hotel.
"Regarding that but also regarding the end of 90 minutes going into the prolongation, then to do what they did... that's a tremendous, unbelievable achievement of the team."
Holland coach Van Basten was at a loss to explain how his team ran out of steam.
"We were unlucky because yesterday Arjen Robben had an injury so we couldn't start with him and then we didn't start well," said the 43-year-old.
"We didn't play football as we did in the first three matches. I don't know why.
"They were a little bit nervous, I think. In the second half we tried something with Robin van Persie instead of Dirk Kuyt so we could be a little more dangerous.
"But the Russians played very well. We had a lot of problems with their attackers Pavlyuchenko and Arshavin."
The Oranje had been mightily impressive in storming to top spot in the 'Group of Death' with thumping wins over Italy and France, and tipped as potential winners by many pundits.
Van Basten, who made no secret when he took over four years ago that Euro 2008 was the main goal during his tenure, will now step down from his role at the national helm to become Ajax coach.
And he conceded it was not the swansong he had hoped for, or the ending he hoped to provide for retiring goalkeeper Edwin van der Sar.
"I feel sorry for Edwin van der Sar because I really had to give him a very nice finale to his career with the national team," said Van Basten.
"We didn't succeed in that and I feel sorry for Edwin because he is a great goalkeeper and he deserved to win with this team a tournament like this."
Van Basten was big enough to admit his side had been beaten by the better - and fitter - side on the day.
"They went 1-0 up. We tried everything. In the end we reached 1-1 which gave us a little bit of hope," he said.
"But we had to change Khalid Boulahrouz because he wasn't good enough physically and we also brought in (Ibrahim) Afellay to play some more football which helped us.
"In extra time we had problems physically. Three or four players couldn't give any more. The Russians were at that moment stronger.
"We tried everything but couldn't hold onto 1-1 and they made two good goals and in the end deserved the victory. They played very well and I wish them good luck in the last part of the tournament.
"They were better than we were today."