Levein opted for a formation designed to frustrate their hosts and hopefully return home with at least a draw to add to the four points gained against Lithuania and Liechtenstein.
The Scots held out for 69 minutes as it looked like his plan might pay off but Roman Hubnik earned the Czechs their first victory in the section, and Levein's men must now pick themselves up ahead of the visit of Spain next week.
The build-up to the match had been dominated by headlines about Levein's decision to axe Kenny Miller, with the Scotland boss furious the news was leaked before he had named his team.
The Rangers striker has been in fine form this season but had to settle for a place on the bench instead, along with Phil Bardsley who was called into the squad after switching allegiance to the Scots.
Levein received an injury boost ahead of the match, with goalkeeper Allan McGregor, Alan Hutton and Steven Whittaker all passed fit, while QPR's Jamie Mackie made his national team debut after being called up to the squad for the first time.
The Czechs had a chance to apply some early pressure when David Weir fouled Tomas Necid 25-yards out but Lukas Magera's free-kick failed to get past the wall, as around 8,000 Scotland fans breathed a sigh of relief.
Steven Whittaker was booked for a foul on Tomas Rosicky after just 13 minutes, before Necid went to ground in the box claiming he had been tripped by Stephen McManus - but pleas for a penalty were ignored.
Necid then earned himself a caution for diving after throwing himself on the turf just outside the area less than a minute later.
The home nation were still looking dangerous and Rosicky saw his angled drive fall inches over the crossbar, before Jan Polak tested McGregor with a powerful effort.
Chances from Scotland had been few but they carved out an opportunity when James Morrison embarked on a surging run before finding Gary Caldwell. He tried to set up Mackie but Petr Cech was able to intercept before he could unleash the shot.
At the other end, McGregor did well to smother a header from Hubnik after he had thrown himself in front of a ball from the right from Jaroslav Plasil, and the goalkeeper then combined well with McManus to deny Necid just before the break.
McGregor came to the rescue for Scotland again shortly after the restart when Rosicky picked out Michal Kadlec from a corner and the Rangers number one managed to tip his header just over the crossbar.
Graham Dorrans then had the ball in the back of the net for the visitors but the offside flag was raised before he even unleashed the shot.
Whittaker proved wasteful with a shot from distance that was well off-target, with the Scots hoping to snatch the opener having successfully frustrated Czech Republic so far.
But it was proving to be a busy night for McGregor as he again ensured the scoreline remained level with a wonderful save to push a Jan Polak header past his right-hand upright.
However, McGregor was helpless to prevent the home side taking the lead after 69 minutes. A Rosicky corner was nodded on by Roman Bednar for Hubnik to bullet a header into the back of the net.
With 15 minutes to go, Chris Iwelumo and Miller - earning his 50th cap - were thrown into the action in the hope of salvaging something from the game.
Barry Robson also came off the bench but Scotland suffered another blow when he picked up a booking which rules him out of the clash with Spain at Hampden.