Two set-piece goals ended Scotland's World Cup dream following a 2-2 draw in Slovenia after a Leigh Griffiths strike had put them 45 minutes from a play-off place.
Griffiths finished brilliantly in the 32nd minute to put Scotland en route to a victory that would have guaranteed second spot in Group F and a two-legged decider next month.
But Slovenia substitute Roman Bezjak twice took advantage of slack marking and Scotland could not find a winner after Robert Snodgrass levelled in the 88th minute, although the substitute came close in the dying seconds of stoppage time.
Slovakia's 3-0 victory over Malta saw them jump into second spot in Group F on goal difference and extend Scotland's absence from a major tournament beyond 20 years.
Gordon Strachan started with two strikers at the Stozice Stadium in Ljubljana with Chris Martin joining Griffiths up front as he matched the hosts' 4-4-2 formation. James McArthur also came in after James Morrison suffered an injury in training on Saturday night with James Forrest dropping to the bench following Thursday's last-gasp win over Slovakia.
Slovenia went into the game with very slim hopes of qualifying - they needed Malta to take a point from Slovakia as well as winning themselves - but they had not conceded a goal at home in the whole campaign.
The home team had the better of the early exchanges and Craig Gordon made a couple of early saves before Andy Robertson set up Martin with a deft pass. The striker's shot was held by Jan Oblak down at his near post.
Scotland continued to grow into the game and Griffiths netted his fourth goal in five internationals. McArthur headed the ball back in the Slovenia box after Darren Fletcher's cross was half-cleared and Griffiths converted the ball inside the far post from a tight angle.
Scotland saw out the half without major concern but the tide turned after the break. Gordon tipped over Rajko Rotman's long-range strike and he was beaten in the 52nd minute.
The hosts were awarded a soft free-kick on the right following Darren Fletcher's challenge on Josip Ilicic and Bezjak got away from the Scotland captain to head the midfielder's inswinging delivery into the bottom corner from six yards.
Ikechi Anya had been waiting on the touchline to come on and Strachan carried through with the tactical switch as Martin came off. Anya lined up in a wide-left position with Barry Bannan tucking in.
Bezjak soon had another chance after Scotland failed to clear but Gordon got a hand to his deflected effort before saving from Ilicic.
Scotland were being forced deeper but Bannan sent Anya away on a break and the substitute got a shot away, Oblak holding the rising strike.
Scotland were struggling to get forward in numbers and the home side went ahead in the 72nd minute. Ilicic's corner was laid back to the unmarked Bezjak, who rolled the ball into the net from 12 yards.
Fletcher had a glorious chance to level after Tierney's cross eventually bounced in front of him 10 yards out, but the Stoke midfielder sliced his volley just over.
Snodgrass and Steven Fletcher came on as Scotland went for broke with 10 minutes left and they got themselves back in it with almost three minutes left. Darren Fletcher lofted a pass beyond the home defence and Snodgrass beat Oblak to it before hooking home.
Scotland broke dangerously later but Oblak scrambled the ball away as Matt Phillips' deflected pass threatened to trickle over the line.
Gordon made a good save from Verbic before home skipper Bostjan Cesar was shown a straight red card following an assistant's flag, having appeared to continue a feud with Christophe Berra after the pair were both booked seconds earlier.
The visitors had one final chance when Berra headed on a long ball but Snodgrass just could not find enough power to loop his header over Oblak.