The Black Caps have never progressed beyond the World Cup semifinals in five previous attempts, but Vettori hoped his team move on from their upset quarterfinal win over South Africa.
"I think we need to move on pretty quickly from that South Africa game," said Vettori of New Zealand's 49-run win at Dhaka.
"It was obviously a tremendous result for us but Sri Lanka is a completely different prospect. It's a different game so we need a different game plan and a better game plan if we want to succeed."
The 32-year-old Vettori brushed aside criticism of New Zealand not being capable of going one step further in the World Cup.
"We're proud of our achievement. I look at the positives of making the semifinals. Everyone wants to talk about our record of not going on any further, but I think it's an amazing achievement for a small country.
"In the Champions Trophy in 2009 we went one step further and made the final against Australia. So we can look on that and hope it's a starting point for us going past the semis."
Vettori believed this semifinal would be even tougher than their 81-run defeat against the same opponents in the 2007 World Cup semifinal.
"This semifinal's going to be a lot harder because Sri Lanka are playing at home. Maybe five or six of us were involved last time so there's a high turnover of players and it's probably a different thing," said Vettori, who has already said he will step down as captain after the event.
"I'm 32 so I think it's time for someone new to come in. After four years, some fresh ideas and a different voice. I wanted to give as much as I could in that time, and then whoever the next man is, stick around and support him as much as I can," added the skipper who has 281 one-day wickets.
Vettori said New Zealand's change in fortunes after losing 4-0 in Bangladesh and 5-0 in India owed much to new coach John Wright and the players.
"John's been fantastic, but the players took the blame for those losses (to Bangladesh) so I think the players have to take credit for the wins as well," he said.
"So it's been a combination of the two. I've loved working with Wrighty and he's brought a lot of passion to the team. And his knowledge of people over here and grounds has been a tremendous help as well."
Vettori eyes bigger things after semifinal
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