The screen legend - who rose to fame in the 1960s as a comedy actor in the Carry On franchise - died in July at the age of 93 and his funeral was held this week.
Writer James Hogg, who was friends with the star, said Cribbins' send off at Woking Crematorium was "suitably special".
Read more: Stars wish Bernard Cribbins a happy birthday
He revealed that songs that the late star recorded were played at the celebration of his life while Tennant and Tate, who Cribbins worked with on Doctor Who, were among those to speak.
What a suitably special send off. Right Said Fred was playing as we entered the chapel and Hole in the Ground (what else?) was playing as we left. Beautiful tributes from David Tenant and Catherine Tate as well as Bernard's dear friend Molly Hawkyard. Even the sun shone x pic.twitter.com/8zYU0Xyvew
— James Hogg (@JamesAHogg2) September 14, 2022
Hogg shared a picture on Twitter of the Order of Service, which had a picture of Cribbins in a pink shirt and red jacket.
"What a suitably special send off," he said.
"Right Said Fred was playing as we entered the chapel and Hole In The Ground (what else?) was playing as we left.
"Beautiful tributes from David Tennant and Catherine Tate as well as Bernard's dear friend Molly Hawkyard."
"Even the sun shone x," he added.
Cribbins was known for popular children's shows such as Jackanory, Old Jack's Boat and The Wombles, which he narrated.
He played Wilfred Mott in Doctor Who from 2007 to 2010, alongside Tennant as the Time Lord and Tate as his companion Donna Noble.
He was due to reprise that role in the upcoming 60th anniversary special of the hit sci-fi series.
Cribbins' other parts include Albert Perks in The Railway Children and barman Felix Forsythe in Alfred Hitchcock's Frenzy.
Watch: Bernard Cribbins' famous crying moment from Doctor Who