Despite a wave of optimism surrounding Michael O'Neill's side, Davis is confident that the players will remain focused for the rest of the campaign.
"I don't think trying to keep our feet on the ground will be much of an issue," he is quoted as saying by BT Sport. "It may help that we don't see the hype at home but it is great to have that again.
"People have optimism but we know there is another tough away game next month in Romania and the most important thing for us is to continue the momentum."
Tuesday's victory marked the first time in Ireland's history that the team have won all three of their opening matches in a qualifying campaign.