Hamilton will end his 14-year association with McLaren by leaving to drive for Mercedes in the 2013 season.
Whitmarsh has revealed that the former world champion turned down an improved financial deal with McLaren, which suggests that even more money was on the table from their Formula 1 rivals.
"We made Lewis an offer - an offer, which I believe is more money than any other driver at the moment is being paid," Whitmarsh told the official Formula 1 website.
"That leads us to suspect that our competitor and our partner Mercedes-Benz offered a bit more money. I don't know that, but I think for Lewis made his decision."
However, Whitmarsh has acknowledged that there are several other reasons behind Hamilton's decision, which was confirmed in September after months of rumours.
"If I were speculating there are a number of factors, and the prime one, I think, is that there comes a time when a man feels he has to flee the nest," Whitmarsh said.
"I think it was a bit of that and a range of different emotions. He has been with us for so many years that I do not fully understand it."