That has helped fuel more pessimism. And with opener Martin Guptill also out with an injury and the captain, Brendon McCullum, dropping down the order to bat at No6, the home side go into the test with a new opening combination of debutant Hamish Rutherford and Canterbury captain Peter Fulton.
Ross Taylor returns from a self- imposed exile and will slot back in at No4, and Dean Brownlie will drop down one to No5.
New Zealand are far from the settled side the English are. There are five changes to the playing XI which lost to South Africa by an innings and 193 runs at St George's Park in January.
Meanwhile, the touring side's only selection dilemma appeared to be whether to persist with Nick Compton at the top of the order or promote Joe Root to do the job.
Regardless, Cook insists his side will need to play their best cricket in what he believes will be a competitive series.
"In all honesty, the T20 and the one-dayers showed how competitive both sides were," Cook said.
"If we play to our potential we will be a hard side to beat, there is no doubt about that. But with the way sport is you've got to be able to play to your potential to earn the right to get into good positions to win games."
Any complacency that might have been creeping into the the English camp was snuffed out with their three-wicket loss in Queenstown.
"We were a little bit sloppy in that warm-up game but, actually, some of the stuff which came out of it was really positive as well."
Stuart Broad got through plenty of overs and was not held back by his heel injury, and Ian Bell and Matt Prior were in good touch with the bat.
"We were disappointed to lose that game but actually it does not matter. The important stuff starts [today]."
McCullum is, if nothing else, an eternal optimist but he is also realistic.
"From our point of view we know this is a huge series," he said.
"We are taking on one of the giants of world cricket and on the back of a tough South African series as well.
"We know the importance of us showing a competitive and fighting spirit throughout this entire series is of future importance to cricket in this country."
With the Black Caps playing an extra batsman in the test, the decision whether to play veteran spinner Bruce Martin or Bracewell's replacement, Ian Butler, is a curly one. McCullum couldn't or wouldn't shed any light on which way the team was leaning.
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