After weathering a first-half storm, Hearts had their chances to retrieve the tie but could not muster enough to seriously concern the home side.
It was mission impossible for Hearts from the outset as they sought to repair the damage inflicted at Murrayfield a fortnight previously.
The Edinburgh side were under the cosh from the early moments and Paul Hartley reacted well to hook a close-in header from Libor Dosek off the line.
Jan Simek then shot just a foot wide from 25 yards with the Hearts' defence guilty of giving him too much space.
Mauricio Pinilla had Hearts' only first-half effort on target with an early header which Jaromir Blazek dealt with expertly.
But there was a let off for Hearts in the 13th minute when Daniel Kolar's shot took a deflection and thumped against the crossbar with Craig Gordon beaten.
There was another narrow escape after 29 minutes when Tomas Sivok had a free header at a corner, but sent his effort wide when he should have done better.
The home side were well in control, but Hearts improved towards half-time and a mistake by goalkeeper Blazek gave Jamie Mole an opening but the angle was too tight and he failed to take advantage.
Deividas Cesnauskis wasted a good chance to put Hearts in front six minutes from the break when he volleyed high and wide with his left foot when he had a chance at the back post.
Cesnauskis had a better effort a minute from half-time when he guided a shot narrowly wide after Sparta failed to clear a Hartley free-kick.
Mole missed the best chance after 48 minutes when he only had Blazek to beat but he shot straight at the goalkeeper and he diverted it for a corner.
If anything, Hearts looked the more likely to break the deadlock in the second half as Sparta seemed content to sit on their first-leg advantage.
Hearts just could not step it up enough in the final stages to salvage the tie, although substitute Roman Bednar went close in injury-time.