Costa Rica confounded expectations by topping a difficult Group D that also contained Uruguay, Italy and England, before then defeating Greece on penalties in the last 16.
Spot-kicks ultimately proved to be Costa Rica's undoing in the last eight, as the Netherlands eliminated them following a 0-0 draw after 120 minutes.
However, despite his disappointment, defender Gonzalez is keen to retain a sense of perspective on an unexpectedly superb campaign.
He told FIFA.com: "We wanted to surprise the world and Costa Rica too. We wanted to make history and I feel we've achieved that with everything we've done."
Gonzalez also took great heart from how neutrals got behind Costa Rica's on their run to the quarter-finals.
He added: "We've earned the support of the Brazilian fans, who ended up identifying with the way we play, and the backing of the fans who came all the way from home to watch us.
"They gave 100 per cent in the stands and we put in the same effort on the pitch."
