Liverpool fans react on Twitter to Dejan Lovren's Croatia performance
Liverpool defender is on course to feature at the World Cup next summer.
This is Greece's third appearance at the World Cup finals, but they have yet to get out of the group stage - though their international highlight was winning Euro 2004.
Fulham striker Konstantinos Mitroglou had plenty of chances to win it for his team at the end of the match, but failed and Costa Rica went on to win the 1-1 draw on penalties.
Fulham striker Bryan Ruiz starred in what was a special win for Costa Rica over Greece, where the game ended 1-1 and was decided on penalties.