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And Santos insists his players were completely drained by the time extra-time began.
"Of course in extra time we had no organisation and our minds were not sharp due to exhaustion," Santos said.
"We tried to push every way we could to score another goal but in the end it went to a shoot-out."
The first seven penalty takers all put their spot-kicks away, before Keylor Navas capped off a valiant display by saving Theofanis Gekas’ effort and the Greece coach praised the goalkeeper.
"Navas was brilliant," he added. "Without him, the outcome would have been different."
The manager also discussed his sending off, which occurred just before the shoot-out, following an argument with referee Ben Williams.
"It was inexplicable. I can't figure out why. I said something very simple to the referee, that I had walked on to the pitch after the final whistle of extra time to support my players.
"I saw the Costa Ricans did the same but I was punished and sent to the stands."
The Ticos now advance to face Netherlands in the quarter-finals on Saturday July 5 at the Arena Fonte Nova in Salvador. It is the first-ever time that Costa Rica have appeared in the last eight at the World Cup.