Mr Hammond has also played down the prospect, telling Sky News: "I've heard some commentators making this observation, but that's now how I've approached the budget".
But the spectre of a no-deal Brexit hung over the 72-minute statement, with the Office for Budget Responsibility (OBR) warning that failure to reach agreement with Brussels would hit the economy hard.
The Chancellor defended his decision to increase income-tax thresholds in a way which benefits the wealthy more than the worse-off.
Johnson said: "Suppose the public finance forecasts deteriorate significantly next year".
On Monday, Philip Hammond announced what he believes is the answer to the tech titans tax problem, with a measure that goes further than most tax regimes around the world: a new digital services tax which takes two per cent of United Kingdom revenues from profitable tech platforms generating a global turnover of more than £500m. The new tax will apply to packaging that contains less than 30 percent recycled plastic.
However, many are already already criticising the tax as too low, describing only £400 million and two percent as nearly nothing to these companies, which are some of the most profitable and wealthiest in the world, with Amazon and Apple the first two companies to ever reach trillion dollar market caps.
But Hammond said further specifics on which programs would get more money would have to wait until next year after Brexit talks are completed.
In Monday's Budget, Philip Hammond abolished Stamp Duty for first time buyers of shared ownership properties worth £500,000 or less.
He told Today: "We retain an ambition to balance the budget".
Although spending on the NHS will rise "substantially" as a result of the "big upward revision" to overall spending plans announced by the Chancellor on Monday, the rate of improvement will be "nothing particularly historic", remaining lower than the average over the health service's 70-year history, said Mr Johnson. If it isn't then the plans for extra spending will look very heroic indeed. Transport for the North is now working on its submission to the Treasury on the project, which has yet to receive formal government approval.
Theresa May has insisted austerity is ending after Jeremy Corbyn claimed public services will suffer hardship for years to come following the Budget.
"Thanks to our careful stewardship of the economy the public finances are in a much stronger position and national debt is falling".
Shares in US-listed Amazon dropped nearly 5% following the announcement.