Alastair Cook's team had to fight to the very last ball, with nine wickets down, to secure even the solace of a 0-0 stalemate at Eden Park on Tuesday. It was an uplifting finale for England, and deflation for their hosts, but will not erase memories of a largely off-colour performance from the tourists over three Tests.
Mutterings of complacency have been aired by observers almost since before the first ball was bowled against hosts ranked six places below England in the International Cricket Council Test table, but Flower said: "There was no complacency in our camp at all. None whatsoever."
He went on: "Your reference to the media talking about the fact we should win easily, or comfortably, is probably where you draw that information from.
"It's certainly not within our dressing room. We knew when we came here we had a real fight on our hands, and we prepared for that.
"We respect the New Zealand cricket team."
Flower does not deny England fell short over the past month of the standards they set, for example, in their historic series victory in India before Christmas.
He is looking forward already, though, to setting the record straight in two home Tests against the Kiwis at Lord's and Headingley in May.
"We have not played great cricket out here in New Zealand.
"But I would say New Zealand have played well. Their bowlers swung the ball continually, and it should make for an interesting series at the start of the summer."