CBS anchor Scott Pelley was furious after John Miller’s scoop about the State Department sex scandal broke not on his “CBS Evening News,” but early Monday on “This Morning” hosted by Charlie Rose, Gayle King and Norah O’Donnell, network sources tell Page Six

There was no mention of the State Department story on “The CBS Evening News” Monday night — and sources say it was because Pelley and his EP, Pat Shevlin, were peeved. Pelley strongly denies this, insisting, there was simply “not enough time” on his broadcast to cover the story.

On Monday night Pelley had Miller in the studio and led with multiple pieces on the NSA leaker. Then Pelley said, “And now to the day’s other big story ……Nelson Mandela.”

A CBS source told us, “CBS had been working on the story for a few weeks, and had been waiting for comment. Finally, [CBS News president] David Rhodes said, ‘We’re doing it.’

“Every other news outlet picked the story up. CBS had it on its Web site all day, so it was astonishing for Pelley not to even mention CBS’s own exclusive scoop on the ‘The CBS Evening News.”

On Monday morning Miller revealed that officials at former Secretary of State’s Hillary Clinton’s department covered up sexual shenanigans, including an ambassador to Belgium allegedly soliciting hookers and minors, and that at least seven agents in Clinton’s security detail hired prostitutes while traveling with her.

Pelley called Page Six last night to vehemently deny he had a meltdown — then promptly went into a meltdown. He roared, “That allegation is false. How long have you been a journalist? You wouldn’t last ten seconds at CBS News. This is not how reporters do their job. You called my publicist but not me in my office?”

Pelley explained, “We wrote that story for ‘CBS This Morning’ on Friday. ‘CTM’ has two hours of air time, I have 30 minutes. Monday was a heavy news day and we had no place to put the story.”

His CBS rep called the idea of a Pelley snub “ridiculous — Miller and Pelley discussed the story at length on ‘Evening News’ tonight [Tuesday].”