The perceived outsiders defied the odds to beat Uruguay and Italy en route to winning Group D and sealing a place in the second round of the tournament.
"It was a really complicated group of very experienced teams. But we came to fight and compete, and we have done," he told reporters following the 0-0 draw with England in their final group game.
"This was called the group of death, but it wasn't - not for us anyway. I'm so happy for Costa Rica. I know the love they have for football.
"May they keep enjoying it! I've loved the three games. We've played a sure, dynamic football. We're unbeaten, it's historic."
As pool winners, Costa Rica will face the runners-up from Group C in the next round.