Since the pair took charge after Ross Taylor's demotion late last year, New Zealand have won none, lost four and drawn five of their nine tests; and won six and lost 10 ODIs.
White was cautious in his praise of Bangladesh - "we don't want to make excuses for our team" - but added that "they are very competitive, and in their home conditions".
McCullum and Taylor are skipping the Sri Lanka tour, starting straight after New Zealand leave Bangladesh next week. White understands there was no consideration given to reversing that decision in the wake of this week's embarrassing ODI defeats.
And Kyle Mills, who will lead New Zealand in Sri Lanka, insists the losses, by 43 and 40 runs respectively, don't point to a mental block against the Bangladeshis.
He cited the last two ODI series wins against much stronger opponents in England and South Africa.
"Bangladesh are a very good cricketing side in their conditions, a tough team to beat. They know these conditions well but they're a lot different to [New Zealand]," Mills said.
"Everyone is building towards the World Cup and conditions will be a lot different for Bangladesh when they head over, so I don't think it's a mental block whatsoever."
This Bangladesh team isn't even at full strength. The country's best cricketer, world No1-ranked allrounder Shakib al Hasan, has missed both games with dengue fever.
New Zealand's problems this week in Bangladesh have revolved around the batting.
The bowling has been serviceably good, the fielding impressive, the batting limp, with no one taking a grip on proceedings and shaping the contest decisively New Zealand's way.
McCullum's wretched run with the bat isn't helping. A captain needs to be in form, leading on the park in a productive sense as well as being the decision maker.
The skipper is well out of touch. He has now scored 244 runs at 17 in all forms since going to England last May. On this tour it's 68 runs in five innings at 13.
On the up side, allrounders Corey Anderson and Jimmy Neesham have caught the eye, Tim Southee looks in good nick after his injury layoff and, well, that's about it.
One prominent broadcaster asked rhetorically this week whether beating Bangladesh really mattered. Yesterday's talkback hammering directed at the national team, and in particular the senior figures, should have given him a clue.