Buckner died after a battle with dementia.
"As I clear my head and hold back the tears I know I will always remember Billy Buck as a great hitter and a better friend," Valentine tweeted. "He deserved better. Thank god for his family. [I'll] miss u Buck!"
The Dodgers issued a statement on social media about Buckner's passing.
"The Dodgers are saddened to hear about the passing of Bill Buckner, who died this morning after battling a long illness," the team said. "Our thoughts and prayers are with the Buckner family."
Buckner debuted with the Dodgers in 1969. He joined the Chicago Cubs in 1977 and was traded to the Boston Red Sox in 1984.
Hall of Fame pitcher Ferguson Jenkins was teammates with Buckner in Chicago from 1982 to 1983. Jenkins said he was "extremely heartbroken and deeply hurt" by Buckner's passing.
Former Mets outfielder Mookie Wilson, whose ground ball led to Buckner's infamous error in the 1986 World Series, said he and Buckner were friends for more than 30 years.
"I felt badly for some of the things he went through," Wilson said in a statement. "Bill was a great baseball player whose legacy should not be defined by one play."
Longtime Mets first baseman Keith Hernandez said he was "saddened" to hear of Buckner's death.
"69 years is too young," Hernandez tweeted. "I know from my mother who also suffered from dementia, that he is in a better place."