The Central Americans were beaten 4-3 in a penalty shootout following a goalless draw in Salvador.
Pinto has admitted that his side were fortunate to end the game level after extra time, but he has praised his players for their unbeaten run to the last eight of the tournament.
"We are proud of what we have achieved," Pinto told reporters following the match. "We leave the tournament unbeaten and with our heads held high. It can happen to make mistakes in a shootout and we did all we could against great players.
"It's true we defended well and were also a little fortunate, but we had faith in ourselves."
Costa Rica had failed to advance beyond the last 16 in their three previous World Cup appearances.