He took over from Matt Smith, who played a younger version of the royal in series one and two.
Speaking to The Guardian's Today In Focus podcast, Menzies said: “There's a lot of different forces at play within him.
“He was someone who was very wary to show his feelings and yet, atmospherically, he's not a cool presence, he's quite hot... He's abrasive.
“He's challenging. He's funny. But there's an energy about it: it's not calm, it's not gentle. And those things seem to be kind of warring inside him.”
Menzies said that Prince Philip managed “a high degree of dignity and patience” for a role he was “clearly not comfortable with”.
“The idea of this alpha male spending his life walking two or three steps behind his wife ... to be in an almost entirely ceremonial position, it's fascinating,” he said.
“It's the stuff of Greek drama. [It] is to his credit, the effect he's had on that institution, on that family.
“He took that completely non-role incredibly seriously, applied a huge amount of energy and inventiveness, and created a life for himself with great ingenuity and great energy.”
Menzies also paid tribute to Prince Philip shortly after the news of his death, aged 99, on 9 April.
“If I know anything about the Duke of Edinburgh I'm fairly sure he wouldn't want an actor who portrayed him on TV giving their opinion on his life, so I'll leave it to Shakespeare. ‘O good old man! how well in thee appears The constant service of the antique world...’ RIP,” he wrote.
Smith, who played the part for series one and two, also offered his own tribute, commenting: “Prince Philip was the man. And he knew it. 99 and out, but what an innings. And what style.
“Thank you for your service old chap – it won't be the same without you.”
Additional reporting by Press Association
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