This clash followed on just days after the drawn first Test at Lord's. But the final match of this three-Test series doesn't get underway until June 5 at Trent Bridge.
Between now and then New Zealand have a three-day tour match against Northamptonshire, starting on Friday.
Vettori hopes this will give his side a chance to lick their wounds whilst allowing the likes of middle-order batsman Daniel Flynn, who played no further part at Old Trafford after being hit on the head by a James Anderson bouncer on the first day, an opportunity for time in the middle.
"We are lucky we do have that warm-up game," Vettori told reporters after England had won a match which New Zealand dominated early on with more than a day to spare.
"If we rolled straight round into a Test match three days later than there would be some guys who were still reeling from this loss. Hopefully, that warm-up game is a chance to get a few things out of the system.
"Then we can come to Trent Bridge thinking we can square the series. That will still be a good result for us," said Vettori, whose side were beaten 2-1 in a Test campaign by England in New Zealand in March.
The Black Caps had initially been hopeful that Flynn would be able to bat again. But bouts of nausea and illness kept the 23-year-old Northern Districts left-hander out of the firing line.
"He hasn't been in a great space the last couple of days. He wants to bat but it just wasn't a good idea," said Vettori.
"He's got some cosmetic surgery to have and, depending on how he recovers from that, it's a great idea for him to get straight back into it."
For much of this match New Zealand, who saw Ross Taylor score a career-best 154 not out in the first innings, looked well-placed to record what would have been only their fifth win in 49 Tests in England.
But a second innings slump, when they were bowled out for just 114 with Vettori's rival left-arm spinner Monty Panesar taking a Test-best six for 37, allowed England back into the game.
Although the hosts' target was an Old Trafford Test record 294 it should have been much greater and England, with opener Andrew Strauss scoring 106, completed their run-chase off the last ball before tea on the fourth day.
As well as being a man down in Flynn's absence, New Zealand's second innings suffered further disruption when all-rounder Jacob Oram was unable to bat in his usual No7 position after sustaining a neck injury during fielding practice.
Oram, who scored a century at Lord's, only made seven and Vettori said: "I don't want to make excuses for a poor batting performance but there's little bits that play their part throughout the game.
"Guys not batting in their normal positions never helps and taking one of your top six out of the equation, who knows he (Flynn) might have scored 30 or 40 runs.
"But it was a very poor batting performance. It's on us, not the injuries."
Vettori praised the displays of Taylor and Iain O'Brien, who bowled well into a stiff breeze reminsicent of conditions at his 'windy Wellington' home ground after replacing the ill Tim Southee.
"Ross Taylor was fantastic in the first innings and the way Iain O'Brien bowled into a very tough wind, those were things that stood out."
However, the disappointed Vettori added: "I don't think they matter to anyone at the moment."
Meanwhile opposing England captain Michael Vaughan was heartened by the way his team recovered from a weak position.
"A young side developing showed a lot of character and swayed the game in England's favour in just an hour yesterday (Sunday) and that pleased me more than anything."
The match was also a personal triumph for Strauss, whose century was his second hundred in three Tests.
In New Zealand, the Middlesex left-hander's England career was on the line until his Test-best 177 set up a series-clinching victory in Napier.
Strauss, who was dropped from England's tour of Sri Lanka before Christmas after a run of low scores, said: "I had a long period of time where I had played in every Test match and I'd probably forgotten a little bit how lucky I am and how enjoyable it is to play a Test match for England.
"If ever I need a reminder of that, this Test match is a great reminder," added Strauss, who also top-scored in England's first innings with 60.
"Wins like this are just so special and when you're sitting by a fireside when you're retired, these are the sort of days you'll really remember."