The Costa Ricans, who needed at least a draw to go through to the second round, crashed out of the World Cup following the game.
But Brazilian-born Guimaraes was proud of his side.
"We came here to show the world the improvements in Costa Rican football and we showed that against one of the best teams in the world," he said.
"I am very proud and happy with our style - it was a very good game and very exciting.
"But I am sad because we have to leave the World Cup. We showed enough football to be part of the World Cup, but that's the law."
Costa Rica finished level on four points with Turkey in Group C, but with an inferior goal difference.