Ole Gunnar Solskjaer was sacked in the aftermath of United's humiliation at Vicarage Road on Saturday, which followed a number of embarrassing defeats.
Ronaldo has cut a visibly frustrated figure during United's dismal run of results, despite scoring nine goals in 13 games since returning to Old Trafford in the summer.
talkSPORT understands the 36-year-old has been left shocked by the state of the club compared to his previous spell under Sir Alex Ferguson.
And according to our correspondent Alex Crook, agent Jorge Mendes phoned Ed Woodward after the Hornets defeat to demand change.
"Ronaldo clearly wields a lot of power," Crook told Jim White on talkSPORT.
"His agent, Jorge Mendes, got in touch with Ed Woodward in the aftermath of the Watford defeat and said, 'What are you going to do about this?'
"Because Ronaldo, I know, has been absolutely flabbergasted by the drop in standards from when he was last at Old Trafford under Sir Alex Ferguson.
"There were players not turning up to training, players not putting full effort into training sessions.
"And, by and large, the same players were getting picked week-in, week-out.
"They've had four very damaging defeats [to Leicester, Liverpool, Man City, Watford] and seven of the XI started all four games.
"What sort of message does that put out to the likes of Donny van de Beek, Jesse Lingard, Anthony Martial, who aren't playing?
"Players that have let their manager down, let the fans down - still get picked? Ronaldo can't get his head around that and he's not the only one."
Publicly, Ronaldo has come out in support of Solskjaer, tweeting a message of gratitude to the Norwegian following his departure.
The Portugal icon said on Twitter: "He's been my striker when I first came to Old Trafford and he's been my coach since I came back to Man United.
"But most of all, Ole is an outstanding human being. I wish him the best in whatever his life has reserved for him.
"Good luck, my friend! You deserve it!"