The Southampton midfielder has spoken of the team's disappointment to only draw with Luxembourg in their last match and, despite the odds being well and truly against them, he believes his side are due some much-needed luck.
The 27-year-old is hoping they can use the frustration from their previous games as inspiration against Paulo Bento's men and kick off their campaign.
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"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."
The Northern Ireland squad has been involved in some famous giant killings, with victories over Spain and England under Lawrie Sanchez's reign the most memorable, and Davis, who featured in those games, believes his side remain capable of replicating that level of performance.
"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," Davis added.
"It's not easy, but we are definitely due a good result."