The warning came from Finance Minister and Deputy Prime Minister Bill English at the National Party's Mainland (South Island) conference in Oamaru on Saturday.
Mr English said the Budget was "only the first step" in the Government's long term plan to make New Zealand "more ambitious and more inspirational".
"It's important we keep the high-level picture in peoples' minds," he said.
Mr English said some people who would pay more because of Budget announcements were cigarette smokers, owners of multi-rental housing, commercial and industrial properties and foreign owners of New Zealand assets.
The tax changes provided a strong incentive for people who wanted to get ahead to save rather than spend too much.
At the same time, the Government had moved to close tax loopholes, a move which would impact on high income earners.
Mr English had a warning for public servants who wanted more money for Government departments.
"Most public servants are getting no extra [this year] - and not next year either," he said.
However, within existing budgets there were opportunities to move expenditure from low priority, "back office" spending to "front line spending".
In his address to the conference yesterday, Prime Minister John Key outlined the steps taken by the Government since the 2009 Budget and in the past 18 months, then reiterated the aims and objectives of last week's Budget.
"The Budget on Thursday was very firmly focused on looking forward and building on the recovery to create jobs, build productivity and attract investment," he said.
"It was also about creating opportunities for families to get ahead in New Zealand."
It was aimed at lifting the long-term performance of the New Zealand economy, reforming the tax system to make it fairer and more sustainable, providing better incentives to work harder and develop skills and to save rather than spend.
Under the previous tax system, if a person earned $39,000 they paid a top tax rate of 33c in the dollar.
Under the Budget changes, those earning up to $47,000 would now pay 17.5c in the dollar.
That meant that three-quarters of New Zealand's wage and salary earners would now pay a top rate of 17.5c.
Families with two children earning less than $50,000 would pay no tax, because of the assistance they received from the Working for Families programme.
Mr Key rejected criticism of tax cuts for the wealthy.
He said many wealthy people did not pay the top tax rate, as they channelled money into trusts.
The only high income-earners on the top tax rates were those who paid PAYE income tax, such as doctors, and the tax changes in the higher bracket were aimed at retaining those professional people in New Zealand.
