Los Ticos secured their path to the last 16 of the competition with victories over Uruguay and Italy, while they rounded off their Group D campaign with a goalless draw against England.
"We're dreaming; we're living a very special moment," the 27-year-old goalkeeper is quoted as saying by Goal.com. "We have to carry on with the same mentality.
"We are happy to have gone through as first in the group. It was something we wanted in our heart of hearts and something we believed in.
"Time will tell how far this team can go. We will stay humble, concentrate on the last 16, which for us is exciting to be there. We want to get through to the quarter-finals, but we know it will be difficult. We have to keep working hard as have been in training and give everything in the match."
Costa Rica last progressed through the group stage in 1990.