In reply, New Zealand struggled to overcome the first over loss of Luke Ronchi for a golden duck and, although Kane Williamson struck an assured 87, his teammates were slowly picked off by England's impressive attack.
Morgan feared England didn't have enough runs to play with after being sent into bat by Williamson.
It therefore needed Wood and Co to step up, and Morgan said: "Guys like him are so valuable to the team - and you can't leave any of our bowlers out".
"I think maybe in the India and West Indies series I was short of runs", he said.
The New Zealand side meet Bangladesh in Cardiff on Friday night (NZ time) in their final pool match of the one-day cricket worldwide competition, with England and Australia facing off in the pool's other fixture.
Although pleased with England's bowling performance - with all five bowlers taking wickets - Morgan was less satisfied with the batting. "So pretty average. So I thought the bowlers today as a collective unit were brilliant, really", Morgan was quoted as saying by the official website of the International Cricket Council (ICC) on Wednesday.
Bangladesh and New Zealand have one point each from two matches and Friday's game will be a must-win for both of them.
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"Of course they do - any England-Australia game is a huge game", he said. Throughout that partnership, I thought Kane and Ross played well, but we still sort of created half chances where a diving catch or a ball just going to hand wasn't too far away. We never take any position that we've ever been in, for granted.
Morgan also praised leg-spinner Adil Rashid, who had figures of 2/47 from his 10 overs.
New Zealand have faced England nine times earlier in familiar conditions in the past four years and England hold an edge over New Zealand with the head-to-head tally reading 5-4. I'm not sure why that is.
Bangladesh opener Tamim Iqbal has been in sublime form in the ongoing Champions Trophy, but his side are in a hard situation when it comes to qualifying for the semi-finals.
Morgan promised no let-up against World Cup champion Australia as England, in marked contrast, seeks its first major 50-over title.
"We now know we have qualified for the semi-finals but we want to be going there on the back of a win and we will be desperate to do that on Saturday", Buttler said, as quoted on CricBuzz. But to be fair to the New Zealand bowlers, neither of the white balls swung at all, and it barely moved off the straight either. "They seem to produce limited-overs cricketers at will", the former Ireland global added.
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