Scott was found dead on Sunday (August 19) after apparently committing suicide by throwing himself off a Los Angeles bridge.
(Tony Scott is pictured above with 'Man on Fire' star Denzel Washington)
The filmmaker is perhaps best known for his directorial work on the films Top Gun, True Romance and Days of Thunder, but he also produced the CBS series Numb3rs with brother Ridley Scott.
Krumholtz - who played math genius Charlie Eppes on the crime drama - has now written of his grief over Scott's passing on Twitter.
"[Tony] was wild and big and crazy and uncontrollable and he gave it his all, every moment, because he believed in his crew, his cast and the show," the actor wrote.
He continued: "It saddens me that something inside him told him to take his incredible life spirit away from us, from the film making community."
Krumholtz's full blog can be read here.
Ron Howard, Edgar Wright, Rosario Dawson, Stephen Fry and Elijah Wood have also paid tribute to Scott's life and legacy on Twitter.
The Raid director Gareth Evans told Digital Spy that Scott's death is a "a big, big loss for cinema" and that he "defined action in the '80s and early '90s".
Scott is survived by his wife Donna Scott and twin sons Max and Frank.
Watch Digital Spy interview Tony Scott about Unstoppable in 2010 below:
Tony Scott's career in pictures:
Copyright: Rex Features MGM/Everett