Dimitar Berbatov and Robbie Keane, who now have 36 goals between them this season, struck in the first half at the Strahov Stadium to provide a cushion for Juande Ramos' side as they prepare for the Carling Cup final.
In sub-zero temperatures in the Czech Republic capital, Spurs were cruising until Cerny dropped the ball under his crossbar and David Strihavka finished.
Tottenham captain Keane lamented a poor second half after his side failed to kill off the tie.
Asked whether Spurs should have put the tie beyond Slavia's reach, Keane told five: "We certainly should have.
"In the first half we played brilliantly, they didn't get a sniff.
"We came out in the second half and I don't know what happened, we knew they would come out and make it difficult for us. The second half performance was not good enough."
As for Cerny's mistake, Keane said: "Things happen, he made a mistake but he's big enough to accept that.
"We've won the game, that's the most important thing. But we wanted to get the job finished today.
"There's still a bit left in this game, we'll get them back to White Hart Lane and there's no reason why we can't go through."
Spurs coach Ramos refused to turn on Cerny.
"The mistakes can always happen, that is the world of football," said Ramos. "This time it was the turn of Cerny.
"It's quite possible that he seemed really nervous after the goal, more than normal.
"It must be very difficult for him to be at his home ground to play against his former club."