The London-born film star, 67, said he felt "very emotional" after accepting the honour from the Prince of Wales at Windsor Castle on Tuesday.
The prince told the actor that every time he sees him on screen as veteran MI5 agent Jackson Lamb in Apple TV's Slow Horses, "I just want to give you a good wash", Sir Gary said.
The actor said he joked in reply: "Well, I think I've scrubbed up OK today."
Slow Horses is based on the Slough House book series by British writer Mick Herron.
Sir Gary is known for his versatile acting, having portrayed a range of figures from former prime minister Sir Winston Churchill to Sex Pistols member Sid Vicious.
"It was emotional. Very emotional. We spoke (for) a minute, but I almost couldn't find my voice," Sir Gary said after being awarded the knighthood.
Of his conversation with the prince, Sir Gary said: "He mentioned The Fifth Element and Churchill of Darkest Hour."
Sir Gary said it was "a lot of fun" playing Jackson Lamb, adding: "He's got sort of an acid wit, sarcastic, he drinks too much, smokes too much, eats all the wrong things.
"Who wouldn't want to play that?"
His directorial debut, a semi-autobiographical piece about his childhood titled Nil By Mouth, was released in 1997 and lauded as a brilliant but gut-wrenchingly emotional film.
The acclaimed film earned him Baftas for outstanding British film and best original screenplay in 1998.
He was lauded for his performance as George Smiley in 2011 film Tinker Tailor Soldier Spy, which saw him earn Bafta and Oscar nods.
But he was unable to secure the leading actor gongs until his role in The Darkest Hour which saw him sweep the 2018 awards season, winning an Academy Award, Bafta and more.
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