"Madiba was an inspiration to the Proteas in the same way that he was to other South African teams," Smith said on Friday.
"To us he represented so many of the qualities which we as players have looked to adopt in playing for South Africa.
"As the captain, I was very privileged to spend some time with him and I vividly recall telephone calls I received from him wishing us luck before a big match or event.
"He always gave simple but wise advice and this had a big impact on me as leader of the team. His words will stay with me forever as they were not only relevant to cricket, but also to life."
De Villiers echoed Smith's sentiments, adding that the Proteas would honour his memory during their current series against visiting India.
"We often felt, especially in my early days in the Proteas, Madiba showed a personal interest in the team and in us as individual players," De Villiers said.
"This motivated us to be better. His memory will not only inspire us in our current series against India, but also to always stick together as a team representing a nation into the future. We will miss him."
Mandela died on Thursday night at his Houghton, Johannesburg, home surrounded by family. He was 95.