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. 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."