Smith dropped the bombshell in his weekly press conference ahead of Saturday's game against Wakefield Trinity.
The players were informed at the end of training on Wednesday morning, an hour before Smith addressed the media.
"I was shocked and I think everybody in the room was shocked," said King, who was handed his Super League debut by Smith at Warrington Wolves.
"When someone as high in calibre tells the group he's leaving it's obviously going to be upsetting.
"It's really disappointing and he's going to be sorely missed, especially by myself. What he's done around the club has been fantastic.
"He's obviously got his own personal issues and that's fair enough, but us players have to stay professional and grounded.
"All we can do is get on with the job at hand. We've just got to do it for the club."
The shock announcement came on the back of a fifth straight victory for the Robins at Toulouse Olympique on Easter Monday.
Rovers are sixth in Super League after ending an eight-year wait for a play-off campaign in 2021, while they can look forward to a Challenge Cup semi-final against Huddersfield Giants in early May.
It is a far cry from the relegation battle Smith walked into when he took over in 2019, with the 55-year-old in the process of leaving an indelible mark on the club.
King says there is a determination in the group to send Smith off on a high.
"We're professional sportsmen and we'll get our heads around it," added King.
"Give us a day or two and we'll be ready and firing come Saturday because we want to give him a good send-off.
"We're still in the Challenge Cup and we're doing OK in the league, although we wish we were doing a bit better.
"We're slowly building something so hopefully we can win some silverware.
"I had some good times with Tony at Warrington and we've been on a special journey. I don't think Tony would want to settle it here and neither do I.
"Long may it continue and let's finish off on a high."
King was on the periphery at Wakefield when Smith asked the front-rower to join him at Craven Park in September 2020.
The 27-year-old is now in the form of his life, something he puts down to Smith's man management.
"It's more the off-field stuff that fans don't see," he said.
"It's not just being a good rugby player but a good person as well. He makes you a good person around the place and makes sure you've got your education in order. It's about after rugby as well with Tony and how you conduct yourself.
"I'm going to speak highly of Tony now - it's not just what he's done for me but other players as well and half of the coaches in Super League can thank Tony.
"He's such a calibre of person I can't speak highly enough of."