A service attended by family and friends was held at the St John the Evangelist Church near his home in Shirley, Croydon, south London.
The candle display referenced one of Corbett's most popular sketches as part of The Two Ronnies alongside Ronnie Barker, known as Four Candles - or Fork Handles.
Stars including Barry Cryer, Sir Michael Parkinson, Harry Hill, Jimmy Tarbuck, Rob Brydon and David Walliams were among the mourners.
After the ceremony, Sir Michael said the service "hit exactly the right note", adding: "It was the least showbizzy funeral I've been to."
He said: "He wasn't a very showbiz person in that sense. He was unaffected by fame and recognition. It didn't bother him."
Sir Michael said Corbett was "a serious man, he was an intelligent man", adding that he was a "stickler" for manners.
The former chat show host said that when comedians die "all that remains is the echoes of forgotten laughter".
Sir Michael said of his friend Corbett: "What you saw is what you got. He was modest, self-effacing, he was a brilliant comic, very good actor too, very good comedy actor.
"And as a guy to be a friend of, he was just unbeatable."
Sir Michael said he will be "greatly missed", adding: "It's a sad day."
Before the service, Tarbuck said Corbett was a "great guy" and added that the atmosphere would be "very sad for the family and for all his friends".
He went on: "He was much loved. Very correct guy, very funny fellow. Disciplinarian - I think that was because he was an officer in the RAF. But he was great company.
"I mean, he was a terrific laugh. Dreadful giggler. He used to get me at it when we worked together."
Prompting cheers from mourners nearby, Tarbuck said: "Much loved, and should have been knighted. That's definitely my opinion."
Corbett's coffin was adorned with white flowers, and the service ended with a recording of him singing Up's The Only Way To Go.
His final words in the song are: "God bless. Goodnight."
In a tribute during the service, Corbett's daughter Emma said: "This is undoubtedly the hardest thing I've ever had to do. And yet it is also a huge privilege."
She joked that the family had borrowed ideas from orders of service her mother had collected over the years, adding that the quote "Grief is the price we pay for love" was taken from Sir David Frost's service.
"My dad was truly loved. Yes, by the world - and as a family we have felt that with so many kind gestures and flowers and thoughts - but however today is not about Ronnie Corbett the national treasure - it's about Ronnie Corbett the husband, the father, the grandfather and the friend.
"He was loved and cherished and it is an enormous honour to be his daughter.
"His integrity, kindness, style and grace were ever present and never left him, even in death," she said.
The star's daughter joked about his height.
"For someone known for being short, he would stand next to me seven foot tall," she said.
Canon Arthur Quinn, a friend of Corbett for many years, conducted the service, and paid tribute to Corbett's wife of 50 years Anne Hart and daughters Emma and Sophie.
He said he wanted to underline "the love and care shown to Ronnie by Anne and Emma and Sophie and the grandchildren" down the years, but particularly more recently when he became "increasingly needy".
He added: "This family love is wonderful and needs to be praised."
Canon Quinn said Corbett "made us happy", adding that "just four candles" had been lit for the service - a reference to Corbett's famous sketch.
He said he played golf with Corbett nearly every Monday for many years.
"In all those years, he told me one joke which I'm not going to repeat," he said. "He was really a very serious man. We talked about all sorts of things, including religion," he added.
Sir Bruce Forsyth's wife Lady Wilnelia was among the mourners but her husband was absent. It is understood Sir Bruce, who had performed alongside Corbett, was too ill to attend as he recovers from surgery.
In her tribute, Corbett's daughter Emma said she wanted to thank her "darling" mother "for getting out of bed". According to reports, Corbett's widow suffered a health scare as she prepared for the funeral, and required tests in hospital.
Michael Thornton, a long-standing friend of the family, told the Daily Mail before the funeral: "I'm extremely relieved to be able to say that Anne is okay. They only kept her in for a couple of days for a safety-first health examination, and she is now back home with her family around her."
The cortege moved on to a local crematorium and the service was followed by a private wake at a nearby golf club.
Corbett became a household favourite in the 1970s alongside Barker in The Two Ronnies and continued to appear on screen into the 80s.