Saints were left with a bitter-sweet feeling after beating Harlequins 22-20 at Franklin's Gardens on Saturday.
Jim Mallinder's men managed to claim the win thanks to scores from George North, Alex Waller and Api Ratuniyarawa, as well as seven points from the boot of Harry Mallinder.
But it wasn't enough to earn sixth spot as Saints needed more than a seven-point success or a bonus-point victory to leapfrog Quins.
Saints were to finish seventh in the Aviva Premiership, meaning they will need to win two home play-off matches against teams from the PRO 12 and Top 14 to earn Champions Cup qualification.
But Saints will not enter those play-offs if Gloucester beat Stade Francais in the Challenge Cup final next weekend as the Cherry and Whites would take the play-off spot should that happen.
That would leave Saints playing Challenge Cup rugby next season, which would be a hugely frustrating conclusion to a disappointing 2016/17 campaign.
Saints knew they could have avoided all of those permutations had they beaten Quins by the necessary margin at the Gardens.
But Mallinder's men got off to the worst possible start as, after some concerted pressure, Quins skipper James Horwill powered over.
Nick Evans converted to make it 7-0 inside the opening four minutes and he was soon adding a penalty to the tally after Quins won one at the scrum.
Saints, who suffered an injury blow as skipper Tom Wood was forced off, needed some inspiration.
And they got it, as Mallinder, playing at fly-half, superbly palmed the ball into the path of North, who flew through the gap to score.
Mallinder converted to cut the gap to three points and Evans missed a chance at the other end, fluffing a penalty.
Saints were suddenly alive and after Marland Yarde could only bundle a clever Nic Groom kick into touch five metres from his own line, a lineout was used to send Waller over.
The prop popped up on the end of a slick move and Mallinder converted to make it 14-10 after 25 minutes.
Evans missed another penalty chance eight minutes before the break, but Quins did lead again soon after as they moved the ball through the hands for Joe Marchant to score.
Evans converted, but that was quickly cancelled out by a Mallinder penalty, leaving it all square at half-time.
It was a nip and tuck start to the second half, but Quins went back in front through an Evans penalty.
Saints then stepped it up, forcing Quins lock Charlie Matthews into the sin bin for a deliberate knock-on.
Saints put the pressure on immediately and thought they had the score they wanted, but referee JP Doyle had already awarded them a penalty.
Quins were hanging onto their lead with Saints frantically trying to find a way through, but the home side started to lose the ball and with it any momentum they had built up.
But Saints did eventually get the score they wanted as after kicking to the corner, forward pressure told, with replacement Ratuniyarawa powering over.
Mallinder stunned the Gardens by hitting the post with a simple-looking conversion, but Saints had a two-point lead, knowing they needed another try.
But despite some late pressure, it wasn't to come as Quins stood tall to secure sixth spot, leaving Saints seventh with the prospect of play-off action later in the month.
Saints: Tuala; North, Tuitavake, Burrell, Foden; Mallinder, Groom (Dickson 67); A Waller, (Ma'afu 67), Hartley (Haywood 70), Brookes (58); Lawes, Ribbans (Ratuniyarawa 67); Gibson, Wood (c) (Harrison 14), Picamoles.
Harlequins: Brown; Yarde (Alofa 74), Marchant, Roberts, Visser; Evans (Swiel 57), Dickson; Marler, Buchanan (Gray 68), Sinckler (Collier 68); Matthews, Horwill (c); Robshaw, Wallace, Luamanu.
Referee: JP Doyle