Midfielder Charlie Adam's first goal since November 24, 50 seconds into the second half, was enough to seal a 1-0 win over Norwich at the Britannia Stadium, providing the club with back-to-back wins for the first time in four months.
Stoke have now hit the 40-point mark long heralded by boss Tony Pulis as enough to clinch safety, although they are not yet mathematically secure of a sixth successive season in the Barclays Premier League.
"You are always pleased when you do hit 40, but we can't relax," said Kemp, standing in for Pulis for the second successive post-game press conference.
"I don't like setting targets. There is a danger in thinking 'well, we've got to 40 we can relax, we can take out foot off the gas'.
"But we've three games to go and we're quite capable of getting 49 points, so let's go for them and we'll look at the table at the end of the season.
"As far as I'm concerned there's still work to do"
At least Pulis, Kemp and the players can at least enjoy a degree of normalcy again after enduring a wretched run of one win in 13 matches prior to these last two successes.
"Like any club, when you win on a Saturday, you can all watch Match of the Day again, read the papers tomorrow. It's a bit more like it," added Kemp.
"When you are losing you lose touch with the outside world because you are not watching TV and reading the newspapers because you don't want to, but we can live a normal life again.
"We were on a bad run, but that's football. You have ups and downs, you have to deal with the difficult periods as well as when things are going well.
"Hopefully we've come through it, we've put two wins together, and now we can look forward to these last three games."
Although Pulis was not available to answer for himself, Kemp feels the Potters boss has handled himself well in recent weeks given the criticism and suggestions he would walk away from the club.
"You don't let it affect you. That's the business we are in," said Kemp.
"If you are the manager of a Premier League club in this day and age, when things aren't going very well, you are a target to be hit - a coconut on the coconut shy.
"But by winning these two games it takes him out of that situation, and we can get back to normal.
"The criticism hasn't affected him or anybody else. But that's the life of a football manager, and you just get on with it."
City's latest slice of away-day misery - they have only won once on the road in the league all season - should have been tripled but for Peter Crouch missing two embarrassing second-half sitters.
In failing to test Stoke goalkeeper Asmir Begovic even once, Norwich find themselves just six points above the relegation zone, and still looking over their shoulders.
Manager Chris Hughton said: "Today [Saturday] we were up against a Stoke side at their most direct and most physical.
"But you know what you are going to get when you come here, and I don't have too many complaints. It's something you have to deal with.
"I thought, if anything, they would get even more direct in the second half and we would have our chances.
"But to concede so early in the second half really hurt us, and with this defeat it means we've still work to do.
"We've two home games, which is a plus, and the situation is still in our hands."