Lumet passed away at his New York home after a battle with lymphoma.
A host of movie stars have paid their respects to the late Lumet, with Goodfellas director Scorsese hailing his death as the "end of an era".
He says, "(Lumet was a) New York filmmaker at heart, and our vision of the city has been enhanced and deepened by classics like Serpico, Dog Day Afternoon and, above all, the remarkable Prince of the City."
Allen describes his old pal as "the quintessential" Big Apple director, adding, "I'm constantly amazed at how many films of his prodigious output were wonderful and how many actors and actresses had their best work under his direction.
"Knowing Sidney, he will have more energy dead than most live people."
Actor Al Pacino, star of Serpico and Dog Day Afternoon, urged film fans to "take good care of the (movies) he left behind", while Phillip Seymour Hoffman, who worked with Lumet on his final film, 2007's Before the Devil Knows You're Dead, credited the moviemaker as "a true master who loved directing and working with actors like no other".
Music mogul Quincy Jones has also offered his thoughts on his late collaborator's death, saying, "Sidney was a visionary film-maker whose movies made an indelible mark on our popular culture with their stirring commentary on our society.
"Future generations of filmmakers will look to Sidney's work for guidance and inspiration but there will never be another who comes close to him."
Jones scored a handful of Lumet's projects after meeting in 1965 while working on drama The Pawnbroker.