Costa Rica gave up a two-goal lead as they drew 2-2 with the United States at the RFK Stadium - American Jonathan Bornstein equalising in the fifth minute of injury time.
The result allowed Honduras, who won 1-0 in El Salvador, to take the third automatic spot for South Africa behind the U.S and Mexico while Costa Rica must now face Uruguay in a tough two-legged play-off.
"First I have to rebuild their spirits. They are in the dumps. This was a shock for them," said Brazilian Simoes, who was in charge of just his second game with the team.
"Everything was going fine up until the last minute. The game just ended and its just very sad. Now we just have to start working again," he said.
Striker Rolando Fonseca said that he believed the team's performance in the U.S capital showed they are capable of beating Uruguay and reaching next year's finals.
"We lost under circumstances that hurt us all but now more than ever it demonstrates to us that whoever we play we will go to the World Cup," he said.
Simoes, who coached Jamaica at the 1998 World Cup finals, missed the decisive final minutes after he was sent off for arguing with the referee and the fourth official and had to be escorted from the bench by stadium security.
The Brazilian said he had argued with the referee about a mix-up when the wrong number was produced for a substitution but the official initially refused to accept the change of number.
"I had to tell him 'please change that' it was a mistake but he didn't accept that. It was unfortunate."
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