Nicks and her Fleetwood Mac bandmates received the MusiCares Person of the Year award at the charity's annual event in New York.
"The loss of Tom Petty has just about broken my heart," Nicks began her speech.
"He did the MusiCares thing last year ... And he spent a lot of time after that night talking to me about how important it was to him," Nicks said.
The singer, who first met Petty in 1978 and called him one of her best friends, spoke about Petty's illness, saying, "He was not well and he fought his way through that tour. He should've canceled and he should've gone home and gone to the hospital."
Petty died a week after playing his final concert at the Hollywood Bowl. Petty's family recently revealed he died of an accidental drug overdose caused by taking a variety of medications he had for his fractured hip.