The 55-year-old will leave Craven Park when his contract expires at the end of the season, a decision that sent shockwaves through Super League.
Smith dropped the bombshell with Rovers well placed in both competitions.
But with Wakefield Trinity up next today and a Challenge Cup semi-final only two weeks away, he has backed his players to shrug off the disappointment.
“We’ll say our goodbyes when it’s time to say goodbye, and now is not that time,” said Smith.
“Now is the time to get on with the competition and the game this week, and not get distracted by any other outside influences.
“I’m 100 per cent committed to the team and the club until hopefully as long as Grand Final day. That would be my preferred final day.”
Smith gave short shrift to the suggestion that the decision could derail the club’s 2022 ambitions.
When the question was put to him, he simply replied: “No.”
Smith will come up against two old friends in Willie Poching and Francis Cummins this afternoon.
Cummins joined Smith’s coaching staff at Leeds Rhinos after hanging up his boots in 2005 and can see similarities with the way his former boss left Headingley.
“Nothing really takes me by surprise with Smithy,” said the Wakefield assistant.
“Maybe the timing of it. I knew he was in the last year of his contract.
“Myself and Willie meet with Smithy a couple of times a year and there was nothing on the cards then; he keeps his cards close to his chest.
“Going back to my Leeds days, he announced he was going to leave at the end of the year and went on to do really well.
“I don’t expect them to put the cue on the rack.”
Whereas Rovers have won five games in a row, Wakefield are smarting from a third straight defeat after being put to the sword by Wigan Warriors.
Cummins was keen to stress that it is a tough ask for Trinity regardless of what has happened at Craven Park this week.
“It doesn’t change anything for us,” he added.
“They’re going to play the way they’re going to play. They certainly won’t be easing off because their coach is leaving.
“We know they’re dangerous with the ball anyway. We’ve been poor defensively the last two games and we can’t afford to do that against this team. They do play and want to throw the ball about.”
Smith, meanwhile, has not been fooled by Wakefield’s recent form.
“They’re a tough team to play,” said the Rovers head coach.
“They’ve got formidable forwards and really good, exciting backs to watch, and half-backs. They’re a dangerous team.
“They’ve had some tough results in the last couple of weeks but if you watch some of the games prior to that, they’re a good rugby league team and are well coached by two coaches that I’ve had experiences with.
“I know they’ll be primed up to get them back on track. They’ll be a really difficult team for us.