Jorge Luis Pinto's men surprised all at the FIFA World Cup, topping the tough Group D ahead of Uruguay, Italy and England.
Costa Rica conceded just one goal – and it came in the 24th minute of their opening game – with a well-organised 5-3-2 formation.
Pinto's side enter their last-16 clash against Greece in Recife on Sunday as favourites, but Gamboa said their approach would remain unchanged.
"You can expect from us for the next game, the same that we have done until now," Gamboa said.
"When we came, and got the results, we were the surprise of the World Cup, now we are not. Now people see Costa Rica like a favourite, and now we have to continue demonstrating the level that we showed in the group stage.
"We have to play a good game, to be intelligent.
"We have studied Greece, so I believe that we are going to play a good match. We have to be the ones with purpose, try to get the result and still going on writing another page of history.
"We are happy but we want more."
Star striker Joel Campbell, out on loan at Olympiacos despite being owned by Arsenal, has shared some of his knowledge of Greece's players with Pinto.
Greece's biggest threat is likely to come from set pieces, but defender Oscar Duarte is confident his team can deal with the danger.
"We have done a great job defending set pieces and corners," Duarte said.
"Uruguay and Italy are good on them, and we stood firm and defended. We have to keep doing the same job, really focused, and I feel that has been a great part of the confidence that we have now."
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