He added: "So I would say to any driver who wanted to win in this sport 'come and join McLaren and aspire to join McLaren'.
"I wouldn't advise anyone to leave McLaren if they want to win, but I've got to respect Lewis's decision and really wish him well."
Hamilton's decision to join Mercedes was announced on Friday and Whitmarsh believes the team, based in Woking, Surrey, could not have offered better financial or competitive incentives for the 27-year-old Briton to stay.
"I know we made a very big financial offer, bigger than I believe any Formula 1 driver is enjoying today, other than himself," said Whitmarsh, who acknowledges Mercedes as a "great" team.
"We were working towards him staying, but we realistically knew there was always a chance he wouldn't.
"He rang me two days ago, from Asia, and I believe I was the first person he told. We had a long conversation, a warm conversation.
"He rang me again yesterday and we had another long conversation. In the end, for all parties, you need to make a decision and move on.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.