Cyclone Sandra ensured a soggy stalemate in the second Test at the Basin Reserve after just 35 overs were possible on Sunday, and then a long-predicted washout settled the issue on Monday. This was a near mirror image of the draw in Dunedin last week.
The upshot is a potential decider at Eden Park, starting on Friday, and both captains appear satisfied with that knife-edge scenario. Cook said: "It's now a one-match Test series. Let's hope we're set fair for five days, and we can actually get a result. Both sides will just want to play five days in a one-off match - and the best side will win."
Cook acknowledged England have so far got no more and no less than they have deserved.
"In Dunedin, we were behind the eight-ball because we didn't bat very well for two sessions," he added. "Then we did well to fight and hold on to that game.
"In this game, we played some really good cricket...but the weather didn't allow us to win. I don't think we've been too far off."
The tourists were 49 runs ahead - with New Zealand 162 for two following on - after rain restricted play to just 35 overs on Saturday.
James Anderson took the only wicket to fall on day four as Kane Williamson and Ross Taylor shared an unbroken stand of 81, and England therefore knew they had only a slim chance of victory - even if the rain stayed away.
Instead, the remnants of Cyclone Sandra did their worst, and a washout was inevitable.
The series score remains 0-0 after the stalemate in Dunedin last week, and a decider is therefore in the offing in the final Test in Auckland, starting on Friday.
Umpires abandoned play at the Basin Reserve at 1405 local (0105 GMT) without a ball being bowled on the final day with the hosts 162 for two in their second innings following on and still 49 runs away from making England bat again.
England had dominated from the outset, batting New Zealand out of the match on the opening day when Nick Compton and Jonathan Trott scored centuries, before their bowlers dismissed the hosts for 254 in their first innings, allowing Cook to enforce the follow on.
It was the turnaround Cook had expected from the No. 2 test side in the world, who had been outplayed by New Zealand in the rain-affected drawn first test at University Oval in Dunedin.
"We got ourselves into a really good position to win the game. We can take a lot from that from our first performance," Cook told reporters after the match was abandoned. "In Dunedin we were behind the eight ball because we didn't bat well for two sessions and we did well to fight and hold on for that game. This game we played some really good cricket and gave ourselves a really great opportunity to win this game but the weather didn't allow us to do that.
"As I said, I don't think we have been too far off, especially in this game."Cook singled out England's pace bowlers James Anderson and Stuart Broad for praise after they had helped the visitors hammer home their first innings advantage when they bowled New Zealand out for 254 in three sessions.
"To bowl New Zealand out for 250 on that wicket was a great effort," Cook added. "The guys were back to their best in putting New Zealand under pressure and not getting away from us.
"That is one of our hallmarks as a bowling attack and we managed to do that."
Broad, who is still recovering from a heel injury that forced him home from India late last year, was the most successful of the bowlers in New Zealand's first innings when he took six for 51.
Anderson did a superb job running into the prevailing nor-wester wind at the Basin Reserve, putting pressure on New Zealand's batsmen and allowing Broad to take the wickets at the other end.
"I think that was his seventh five for (wicket haul) and he ran in the best I have seen him run for a while," Cook said of Broad. "I think he's fully confident now with his heel and as a senior bowler it's great to see him back. I think Jimmy Anderson, though he didn't get the wickets, I think he bowled 30 overs into that wind and ... did such an outstanding job into that wind.
"Stuff like that goes unnoticed. If you're watching on TV you don't realise how strong that wind is. He never complained, well not on the pitch anyway, so it was an outstanding effort."