The most creative moment in the match came in the 56th minute when Aleksandar Kolarov curled a delightful free-kick into the top corner after a foul by David Guzmán on Aleksandar Mitrović, which proved to be costly for the Costa Ricans.
If Costa Rica are going to recover, however, they will need to rediscover the defensive organization and clinical counter-attacks that propelled them to the quarter-finals four years ago.
"It is great to have three points, but we are not finished".
Costa Rica manager Oscar Ramirez insists that Los Ticos' World Cup adventure "isn't over" following their 1-0 loss to Serbia on Sunday.
While not pacing right down to the touchline, Ivanovic tested the Costa Rica defence with his crosses for deep up into Mitrovic and the pushing Milinkovic-Savic.
The 44-year-old admitted he had been under pressure in the build-up to the game.
Australia bowl first in must-win ODI at Trent Bridge
Travis Head top scored with 51 with Marcus Stoinis (44) the only other batsman to score more than 25. Once again it was spin that did the damage with Adil Rashid taking 4-47 and Moeen Ali 3-28.
The critics had seen Serbia as the team in Group E that would be easiest to defeat.
FIFA World Cup 2018 Costa Rica vs Serbia match will take place at Samara Arena in Samara in Russian Federation.
Novak Djokovic insists he would happily miss a first appearance for Serbia in the World Cup final if it means he is back in the Wimbledon title match.
The European nation closed in on a second when Milinkovic Savage found space in the box, but wasted an inviting opportunity to put them further ahead following a dismissal effort.
"That's something that maybe cost us in our friendlies, especially in our last match where we had a hard time dealing with Belgium. I don't want to do the maths yet", Kolarov said.
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