Stevie May's deflected effort three minutes before half-time handed the Perth side a lifeline following their 2-1 home defeat, but they failed to build on their advantage in the second half. A blunder from Gary Miller allowed Martin Mikovic to level with eight minutes left to seal a 1-1 draw for the hosts and a 3-2 aggregate victory.
The goal could be May's last for the club amid talks with Rotherham and reported interest from Sheffield Wednesday but ultimately it counted for nothing as Saints failed to do enough to get the 2-0 win they needed.
However, the Scotland Under-21 striker was inches away from forcing extra time when he threw himself at a cross amid some late pressure from the visitors.
St Johnstone started brightly and home goalkeeper Dobrivoj Rusov was forced into early saves from a Dave Mackay header and a bobbling strike from May, which he fumbled but saw his defence clear.
Alan Mannus soon had to get across his goal to save a bouncing effort from long range from Jan Vlasko before Saints had the first real chance in the 17th minute, but Rusov made a brilliant save from May's impressive effort.
The in-demand striker met David Wotherspoon's lobbed pass on the half volley and powered a left-footed shot towards goal, but the goalkeeper reacted well to dive and touch it over the bar.
Mannus got down well to hold another drive from Vlasko and the Perth side had a let-off just before the half-hour mark. Mikovic got space on the left to cross and Ivan Schranz, who scored twice in the first leg, got there first at the near post but his header hit Mannus and Brian Easton was relieved to see the ricochet clear the bar.
Schranz caused more problems when he cut the ball across goal but left-back Easton covered well.
Saints survived the pressure and took the lead after a charge from the back from Tam Scobbie, who was sporting a bandage around his head after being wounded earlier on.
The defender got the ball to May 20 yards out and the striker fired a left-footed shot that took a major deflection and skidded across the goalmouth and into the far corner of the net.
Saints were still heading out on the away goals rule but they could not mount any sustained pressure after the break, and Mannus made a great save in the 70th minute when he pushed away Martin Vyskocil's header following Erik Sabo's free-kick.
However, Saints had a rare chance to nick a goal but Wotherspoon's free-kick was cleared and the Slovakian side scored on the counter-attack.
Right-back Miller made a mess of clearing a high ball as he back-pedalled and could only head it into the path of Mikovic, who kept his composure to slip the ball past Mannus after being played clean through.
The Scottish side pushed forward in a bad-tempered finale and almost prolonged the encounter in injury-time when Lee Croft sent in a tantalising cross, but May just could not connect.