"I realised I would not be able to count on conditions to carry out my work," the 61-year-old Colombian said on his personal website on Thursday.
"It wasn't possible to reach an agreement," he added. "I ask myself, 'What use are the victories obtained in Brazil?".
Federation president Eduardo Lee confirmed at a news conference that the two parties had not managed to agree fresh terms.
Costa Rica were unbeaten in five World Cup matches before going out on penalties to the Netherlands.
Pinto said disagreements with members of his backroom team became the central issue in negotiations with Lee.
"Some of my staff don't have my style. I've had differences with my staff, I want dedication and commitment," he told the news conference.
"A year and a half ago a member of my staff told president Lee to get rid of me, that with me we weren't going to the World Cup. I slept with the enemy for a year and a half.
"It hurts me to leave Costa Rica because I did an outstanding job here. I demanded the staff be dismissed and they didn't accept," said Pinto of the federation.
Lee said the people of Costa Rica "would always be grateful" to Pinto.
"I want to thank Pinto with all my heart for his work which no doubt was the key to obtaining the successes we got in Brazil," he added. "Unfortunately we couldn't agree on some aspects."
The Colombian, who took charge in 2011, steered the Central American nation to their fourth World Cup finals in his second spell at the helm.
Pinto was previously coach from 2004-06. He also guided his native country between 2007-08.
Costa Rica began the finals with a stunning 3-1 upset victory over twice champions Uruguay in their opening Group D match.
They followed up with a 1-0 triumph over four-times World Cup winners Italy before drawing 0-0 with England.
The 'Ticos' then beat Greece 5-3 in a penalty shootout in the last 16 following a 1-1 draw after extra-time.
Costa Rica were eventually eliminated by the Dutch, 4-3 in a shootout following a 0-0 draw after extra-time.
Pinto will now look at other options after attending an international congress for coaches in Germany, read the statement on his website.
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- Costa Rica