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Arkadiusz Milik scored the only goal of the Group C game in Nice on Sunday, finding the net on 51 minutes.
Northern Ireland failed to register a shot on target and Norwich City forward Lafferty insists the team will "put it right" when they face Ukraine in Lyon on Thursday.
Captain Steven Davis added: "We need to be better on the ball and braver."
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The defeat ended Northern Ireland's 12-game unbeaten run after they had topped their qualifying group for the tournament in France.
"We always knew it was going to be difficult, but we were not good enough," added Davis, who thanked fans for their "incredible support".
Lafferty promised a "more determined" performance against Ukraine, who lost 2-0 to Germany in Sunday's other Group C game.
"That was not the team that has got us here and we didn't turn up," he said.
"The whole performance was not a Northern Ireland performance and on Thursday we will go and put it right."
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Northern Ireland manager Michael O'Neill said the result was "obviously disappointing" but insisted his side could "redeem" themselves against Ukraine.
"We have to acknowledge Poland were the better team," he added. "They never gave us a chance to settle into the game.
"We found it difficult to get a foothold and I think that was partly down to their physicality.
"They were very, very powerful in every area and that's something we're going to have to adapt to very quickly, because I don't envisage Ukraine will be any different prospect in that respect."
Northern Ireland were "overawed" as they began Euro 2016 with a 1-0 loss to Poland, says striker Kyle Lafferty