"We are very much sad," the exiled Tibetan spiritual leader said in a live webcast broadcast organised by the Nelson Mandela Foundation in Johannesburg. "However, this sadness is not much use. This sadness must translate into willpower, determination," to emulate Mandela's example of peace, said the Dalai Lama who lives in exile in northern India.
Mandela received the Nobel Peace Prize in 1993, four years after the Dalai Lama, and the two men last met in 2004 in Johannesburg.
Dalai Lama: Whether the person is alive or not, his spirit should be alive
The religious leader said he was an admirer of Mandela, whom he hailed as a "great person" - not least because of his "ability to share affection".
"So now our responsibility is we must follow his spirit. Whether the person is alive or not, his spirit should be alive."
The Dalai Lama, who has twice been unable to secure a visa for South Africa since 2009, did not attend any of the week-long Mandela funeral events which will culminate with his burial in his home village of Qunu on Sunday.
The last visa refusal was in 2011, when he was invited to give a lecture as part of celebrations for the 80th birthday of Mandela's fellow anti-apartheid campaigner Desmond Tutu. South Africa gave no reason for not granting the visa, but the move was widely seen as a bid to avoid antagonising China, which views the Dalai Lama as a separatist intent on fomenting unrest in Tibet.
Tutu, a retired archbishop, told the online discussion that being in Mandela's presence had been "quite overwhelming". "He was an embodiment of goodness," he said. Mandela, South Africa's first democratically-elected president, died at home last Thursday aged 95.