The Central American nation sit bottom of Group E with no points to their name, but could yet qualify for the next stage if they significantly improve their goal difference in beating Switzerland on Wednesday, and group leaders France beat Ecuador.
And Costly - scorer of Honduras' only goal of the tournament so far - revealed that the team remain confident.
"Hope is the last thing you lose, as they say," he is quoted as saying by FIFA.com. "But we know it’ll be a very tough match against the Swiss because we know their game well.
"We’re still hopeful and we've got faith that everything will turn out well, that’s what we're clinging on to."
Costly also explained his preference for wearing the shirt number 13 - considered unlucky by many.
"First of all I used number 13 because it got given to me," he added. "But then I got a feel for it and it’s been really good for me.
"I’ve always scored goals when wearing that number and now, wherever I go, I make sure I ask for it!"
