Martin Whitmarsh says McLaren offered Hamilton the chance to be the best-paid driver of the Formula 1 field in a bid to keep him for 2013.
Following months of speculation about his future, Hamilton decided to leave McLaren after six seasons with the Woking-based squad. The Briton will join Mercedes to replace seven-time champion Michael Schumacher.
Whitmarsh denied McLaren underestimated Mercedes' offer, saying he believes the terms McLaren put forward bettered any other deal on the current F1 grid.
"I think Lewis is a top flight driver and we didn't underestimate his attractiveness to others in F1," Whitmarsh said during a Vodafone phone-in on Wednesday.
"I think we knew that Lewis would be in demand, that's why we made him an offer. The offer that we made was higher than, I believe, any other driver in Formula 1 is currently receiving, or will receive next year.
"It was a good offer but clearly we had to look at the benefits because we recognised that there was a serious threat."
Despite losing Hamilton, McLaren boss Martin Whitmarsh says he has no regrets about his team's management of its negotiations with the 2008 world champion.
Hamilton's relationship with McLaren began when the team saw his potential when racing in karting.
Whitmarsh said he was satisfied the team had done all it could to retain the former world champion.
"Probably I am not the most objective to give that answer," he said when asked if the situation could have been managed any differently.
"I think we had a lot of conversations with Lewis's management team. I don't think I have any particular regrets.
"I think that we made a very good and serious offer and proposition. Ultimately of course we weren't able to agree terms.
"Probably two things: One, I am not the best person to answer your question and be objective about it and two, looking back and regrets are things you don't get much time for in F1."
He added: "We put a lot of effort in to trying to keep Lewis. Clearly he is a great asset to any race team, so we made a big effort but I think ultimately Lewis had to make a decision, he made one, and we must now look forward."