The Ethniki advanced through to the last 16 with a dramatic 2-1 victory over Ivory Coast on Tuesday night to set up a round-of-16 clash against Costa Rica.
"We found balance tonight," the 59-year-old is quoted as saying by BBC Sport. "We are not the worst team when we lose or the best when we win. To everyone in Greece I say: Go out into the street and celebrate."
Santos was appointed as manager of Greece in 2010.