The brace was a perfect way for Olic to mark his 90th international cap, taking his tally to 18 goals after showing a predator's instinct to overshadow younger and more heralded strikers vying for a place in coach Niko Kovac's final squad.
However, the Wfl Wolfsburg hitman remained humble after a performance that left the likes of Mario Mandzukic, Eduardo da Silva and Nikica Jelavic standing in his shadow.
"We played well in the second half but were poor in the first, which was kind of expected because some of the players have just come off a winter break, are still in one, or are not in the best of shape," Olic told Croatian media.
"We want a quick transition of the ball when we win possession... that's our World Cup game plan and it worked very well in the second half against the Swiss, who showed once again that they are a very good side."
The Swiss, who are in World Cup Group E with France, Ecuador and Honduras, got through qualifying unbeaten, while Croatia were drawn in Group A alongside hosts Brazil, Mexico and Cameroon after a 2-0 win over Iceland in the European playoffs.
Olic, who scored a crucial goal in a 2-0 home win over neighbours Serbia in qualification, was impressed with the performance of Swiss marksman Josip Drmic, who also netted twice in the lively encounter in St Gallen.
But Olic was also disappointed not to have the Nuremberg striker, who has Croatian roots, alongside him at the 32-nation tournament in Brazil.
"I know him from the Bundesliga and from my point of view it's really a pity that he plays for Switzerland and not Croatia," Olic added.
"But he chose Switzerland and I wish him all the best in the future and in his career at both club and international level."
- Sports & Recreation
- Mario Mandzukic
- Nikica Jelavic
- Eduardo da Silva