Kevin Doyle gave Martin O' Neill's men the lead after just 13 minutes, before Celos Borges equalised from the penalty spot in the second-half.
Robbie Keane had the chance to put Ireland ahead again soon after, but had his penalty saved by Costa Rican keeper Patrick Pemberton.
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Meanwhile;
World Cup hosts Brazil will go into the tournament on a back of a 1-0 win over Serbia, but supporters jeered their team, who struggled against their opponents.
Portugal edged past Mexico 1-0, while Croatia were 1-0 winners over Australia.
