Boss Chris Boyd says Saints have achieved a 'pass mark' by securing a top-six finish for the season.
But the director of rugby insists his team will now go and 'throw the kitchen sink' at Exeter Chiefs on the final day as they look to secure a Gallagher Premiership play-off place.
Saints moved back up to fourth, one point above Harlequins, after earning a comprehensive 38-10 bonus-point win against Worcester Warriors at Franklin's Gardens on Saturday.
And they know that a win at Exeter on May 18 will make sure of a top-four spot.
Harlequins go to Wasps on the same day, knowing they need at least two points from the match to have any hope of leapfrogging Saints, who can now look forward to returning to the Champions Cup next season.
"It was the minimum standard for us," Boyd said.
"We never contemplated relegation and we felt the very first pass mark was to get back into the Champions Cup.
"We've achieved a pass mark for the season but we still have our own destiny in our hands.
"We go to Exeter, which is going to be a really tough game for us with the way they play the game, but we're going to throw the kitchen sink at it and see if we can get enough points to get into that top four.
"Maybe someone else can do us a favour in another game, but we're certainly not going to go down there with any other ambition than to have a crack."
Taqele Naiyaravoro scored twice to help Saints sink the Warriors, with Luther Burrell, Tom Wood and Reece Marshall also registering at the Gardens.
And Boyd, who saw his side race into a 28-3 lead, said: "We wanted to get the job done in the first half.
"We knew Worcester had got the monkey off their back in terms of avoiding relegation and they had a short turnaround (having beaten Gloucester last Sunday).
"We knew they would come here with the pressure off, saying 'let's go and enjoy ourselves' so we knew we had to challenge them around our defence and breakdown work.
"If you've got half an eye off the ball in not being really committed to the game it's going to show at the breakdown, and our defence and breakdown work was really good.
"We scored four tries before half-time, but the second half wasn't quite as good.
"We talked about wanting to keep our standards high and we got 10 points in the second half, but the latter part was really about preserving guys and giving others opportunities.
"The forward pack we finished with, you might have been mistaken for thinking it was a Monday night (Wanderers game)."