Menzies held two leads in the match but was pegged back by 20-year-old Manby to force a nervy deciding set where both players missed shots at a checkout.
Manby finally pinned double four as he wheeled away in celebration, the frustration of defeat overcame Menzies as he punched the underside of the drinks table several times.
Referee Kirk Bevins urged the Scotsman to stop before he congratulated Manby for the win, then gestured an apology to the Alexandra Palace crowd.
The top of Menzies' knuckle drew blood from a deep cut as he walked off the stage.
Menzies, though, later offered an apology for his behaviour and how he reacted on Monday afternoon.
"First of all, I would like to apologise for what happened," said Menzies. "I am sorry that I reacted in the manner that I did.
"It's not an excuse, but I have had a lot of things on my mind recently and I suppose it all just became too much at the end.
"It has not been an easy time for me with my uncle Gary passing away recently. I saw him four days before he died and he gave a look which told me how much he thought of me. He treated me like a son.
"Had I won the game against Charlie, my second match would have been on the day of Gary's funeral and that has not been lost on me in recent days.
"Let me say again, that's no excuse for what I did on the stage. It was the wrong thing to do and I don't want it to take anything away from Charlie. He played well and deserved his win.
"This is not how I would like people to view me. Yes, I can get emotional at times, but not like that and that wasn't right."
The PDC's chief executive Matt Porter said the incident will be reported to the Darts Regulation Authority, but the organisation will offer its support to Menzies.
"I spoke with Cameron and his management before he left the venue, and he knows there is support available from the PDC and the PDPA," Porter said.
"Any incident of this nature is reported to the Darts Regulation Authority for review, but our main priority is the player's health and well-being."
It is the second-straight year that Menzies has exited the World Championship at the first hurdle after losing to Leonard Gates last year.
The 36-year-old was left in tears on stage during the defeat to the American after enduring anti-Scotland chants and jeers from the crowd throughout.