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8 year oldThe two sides meet in the last 16 of the tournament on Saturday (17:00 BST).
Real Madrid's Bale, 26, and 28-year-old Lafferty, who plays for Norwich, both scored seven goals in qualifying.
Bale said Wales' "ultimate goal" is to win the Euros, while Lafferty said he believed Northern Ireland "can go all the way" in France.
Chris Coleman's Wales side qualified for the last 16 as Group B winners - ahead of England - while Michael O'Neill guided Northern Ireland to third place in Group C.
They are in the opposite side of the draw to England, current world champions Germany, reigning European champions Spain, four-time World Cup winners Italy and hosts France.
"Obviously you come to the tournament for one reason - to win, not to play three games and go home," said Bale, who is Euro 2016's joint top-scorer with three goals in the group stage.
"The ultimate goal is we want to try and win the tournament.
"It's a cliche but we'll take each one as it comes. Yes, we would love to win it, but all our focus now is on Northern Ireland."
Lafferty, who is yet to score at the tournament, said: "We honestly believe with our heart and determination that we can beat anyone.
"With the squad we have I honestly am sitting here thinking we can go all the way. If we get a bit of luck we can upset a few teams.
"Stopping Bale is the big question. He's a very big part of their team as a player of that calibre is going to be. We'll look at areas where they are strong and areas that we can exploit.
"It'll be interesting to see who it wants it most on Saturday. I believe we'll come out on top."
Prior to their defeat by England in the group stage, Bale suggested Wales had"more passion and pride" than Roy Hodgson's side - and the two-times Champions League winner thinks his team have more in common with Saturday's opponents.
"They topped their [qualifying] group, you don't do that by mistake," said Bale.
"They have very similar team spirit to us. They are a bit more defensive than us -it will be difficult to break them down, but we will try our best."
Meanwhile, veteran Northern Ireland defender Aaron Hughes, 36, expects the supporters of both teams to make the match a memorable occasion.
"It'll be a fantastic game," the 102-capped player said. "I think the atmosphere will be tremendous - as good as any here.
"Everyone has seen how good our fans have been so far and the Wales fans have been similar. One of the best atmospheres I played at was against Wales at the Millennium Stadium in 2004."
Hughes' fellow-centre back Jonny Evans added: "We're in such a position here to create history that can last a long time and we don't want to let go of that.
"We want to go as far as we can and not waste this opportunity."
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