Mercedes confirmed yesterday that Hamilton would be joining them on a three-year deal from the start of the 2013 season, ending a 14-year association with McLaren.
Hamilton will replace Michael Schumacher at the German team, with Mexican driver Sergio Perez – currently with Sauber – stepping in for the Briton at McLaren.
Whitmarsh believes the switch makes it less likely Hamilton will achieve his ambition of matching his hero Ayrton Senna and becoming a three-time world champion.
"Mercedes is a great partner of ours and they are a great team," Whitmarsh said. "But for anyone leaving McLaren, and he wants to win, I think that's a mistake because I have faith and belief in this team.
"Whether you measure it over the last four races, four years or 40 years, we're a fantastic team, so I would say to any driver who wanted to win, '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' decision and really wish him well."
Mercedes have won one of 52 grands prix since taking over Brawn, the champions in 2009. McLaren have won 16 over the same period.
Whitmarsh is adamant McLaren did everything in their power to keep hold of the 2008 world champion, although their initial offer is believed to have represented a pay cut on his current salary.
Whitmarsh added: "We made a very big financial offer, bigger than I believe any [other] driver is enjoying.
"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. In the end, you need to make a decision and move on."
Aside from a reported £15m-per-year salary and greater freedom with image rights and sponsorship appearances, Hamilton is still chasing multiple world titles.
Hamilton said: "I am very excited to begin a new chapter racing for Mercedes.
"I believe that I can help steer the Silver Arrows to the top and achieve our joint ambitions of winning the world championships."
Schumacher, the 43-year-old seven-times champion, now appears on the brink of retirement for a second time after a tough three years with Mercedes, epitomised by Sunday's crash in Singapore.
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