Northern Ireland's first two matches in Group F saw them defeated 2-0 by a strongly fancied Russia and then held to a disappointing 1-1 draw in Luxembourg. The Southampton midfielder knows the odds are stacked heavily against his side, ranked 117th by FIFA to Portugal's third, but he remains hopeful.
"Luxembourg was a big chance to get three points and we were massively disappointed not to," Davis said. "So hopefully something special can happen here and that will kick us off for the campaign."
He added: "We understand what we are up against and need to keep our shape compact and frustrate. Once we get clear possession we must try to interact and cause them problems.
"I think everyone was disappointed after Luxembourg. It was a frustrated dressing room after the game, so this gives us an opportunity to put something right."
"I think there are a number of players in the squad who have managed a few upsets and we need luck and want that if something is to come from the game," he said.
"It's not easy, but we are definitely due a good result."