Yates was in good shape in the Giro d'Italia's opening time trial in Bologna, which, like Sunday's stage to San Marino, also began with a flat section then concluded with a tough climb.
But unlike in Bologna, the British rider shipped a considerable amount of time on stage winner Primož Roglič (Jumbo-Visma) on Sunday, and as White told Cyclingnews, there was no clear reason why.
"I'm not sure, I've not got an explanation for you," White said. "He went out hard and then didn't have a good climb."
White brushed aside the idea that Yates' crash and minor injuries to his left side on stage 4 could have had an effect.
"Mate, we're not making any excuses," White said. "He crashed a few days ago, but it is what it is. We're looking forwards not backwards."
All had been going fine over the flatter roads in the first 22 kilometres of the time trial, where in theory Yates was at a disadvantage.
"His splits to the bottom of the climb were what we wanted but then he had bad sensations on the climb and he certainly paid for it," White told Cyclingnews. "It wasn't the time trialling [flat section] that went badly, it was the way he climbed.
"So as I said, I've not got an explanation, it is what is, he suffered there and lost a considerable amount of time. "
White remains insistent there is time for the tide to turn in Yates' favour again in the Giro, particularly with a long stretch before the mountains so that they can assess what his options really are.
"We have still got plenty of days to go, the race doesn't kick off in earnest again until Friday [on stage 13].
"So we've got a couple of days" – the rest day and the flat stages across Italy early this week – "to lay low and we'll come up with a plan, that's for sure. We're in a situation we didn't plan on being in, but that's racing, isn't it?