Italy coach Cesare Prandelli admitted two missed chances by Mario Balotelli had proved costly as Costa Rica triumphed 1-0 to clinch their place in the last 16.
Bryan Ruiz's header secured a 1-0 win for the Ticos who will qualify from Group D even if they lose to England on Tuesday.
He said: "Mario played well in the first half had two chances and if he had scored then the game would have been different.
"We came into this game with too slow a pace, and Costa Rica were well-organised and so our approach was not of the best."
Asked if he had a message for England, who had been relying on an Italian victory, Prandelli added: "I am terribly sorry not just for the English but also for us as we wanted to win.
"Now we will have to play well against Uruguay in order to qualify. We knew this was a particularly challenging and difficult group and now we have to try to recover our energy for the Uruguay game in four days."
Jorge Luis Pinto, Costa Rica's Colombian coach, said he was now targeting a third win in the group - against England.
He said: "Of course we want to win the next match now and I must ask my players to keep calm and play just as well.
"We knew that we could make history for Costa Rica and today we have done that. That's what I told my players today - let's change history.
"It was a beautiful match and the people of Costa Rica deserve this day. They have supported the team and me and this was for them."