Michael O'Neill's charges were second best in their opening Group C defeat to Poland at the Allianz Riviera.
Ajax's Arkadiusz Milik netted the solitary goal of the contest shortly after the interval and it took until the game's closing quarter for Ireland to trouble Wojciech Szczesny's goal.
'Just not good enough'
Speaking to BBC after the defeat, Davis was forthright in his assessment of his side's display.
"We need to be better on the ball and braver," said the midfielder. "It's a learning curve and we'll learn from it.
We always knew it was going to be difficult but we were not good enough."
Davis squandered a gilt-edged chance towards the dying embers when he failed to make a clean connection with Oliver Norwood's quick free-kick.
Ireland, though, missed the set-piece quality of Chris Brunt -- nursing the injury sustained with West Bromwich Albion in February -- and failed to supply talisman Kyle Lafferty with sufficient service.
Conor Washington was introduced on the hour mark and manufactured an opening but Poland goalkeeper Szczesny was quick off his line to foil the danger.
Poland could have added a second three minutes from time when midfielder Grzegorz Krychowiak unleashed a rasping effort from distance that had Ireland goalkeeper Michael McGovern scrambling to his left.
Onwards and upwards
O'Neill's side face Ukraine on Thursday evening in Lyon and conclude their group stage campaign against the world champions Germany at the Parc des Prince in the French capital.
Thursday night's showdown takes on added significance given that O'Neill's side arrive as heavy underdogs against Germany in the closing group game and O'Neill is sure to have his players fired up.