A mistake in the garage prior to Hamilton's final run in Q3 meant that the British driver did not have enough fuel to be able to complete an in-lap and provide a mandatory sample for the FIA.
But rather than give up on the challenge for pole, McLaren let Hamilton complete his lap before ordering him to stop.
That decision ultimately led to the 2008 world champion being excluded from qualifying and moved to the back of the grid, which was a more severe penalty than the team was expecting.
Speaking about the matter after the race, Whitmarsh said that he should have acted differently.
"With hindsight I was wrong, but I don't think I or very many people anticipated that, as a consequence, we would be starting from the back of the grid," said Whitmarsh.
"With hindsight I could have called it a different way, and he could have just come in at the end of the out lap. But frankly I did not expect the penalty that he received."
Whitmarsh revealed that the team only became aware of the fuel situation once Hamilton was on his qualifying lap.
"Part way through that last qualifying lap, the data indicated that there was not as much fuel on board as we thought," he said.
"We knew there is a black and white regulation that says you have to be able to give a litre [sample] at the end, so I took a call which was: right, that is a black and white regulation, there is no negotiation, let's make sure we can comply.
"We stopped the car and pumped out 1.3 litres as it turned out, but we didn't know that until several hours later. It could have been three litres and I would have been moderately embarrassed. Whatever the outcome I was going to be embarrassed."