Juventus had to wait until the 76th minute for an Alessandro Del Piero screamer to secure the win over the current UEFA and European Super Cup holders.
"The three points were crucial and we paid a little for the fact that we may not be Champions League debutants, but we felt like it tonight," Nedved was quoted as saying by Calcio Italia after the game.
"We will have to wait for other games to play better football, as we needed the result tonight and are happy with it. We know we have to improve, but there is plenty of time for that.”
The game marked Juventus' European comeback after two years of absence following the Calciopoli scandal, and despite the nervy start Nedved was pleased with the game's general outcome.
"I felt a bit nervous and saw some of my teammates who were very tense in the first half. They couldn’t express themselves as well as usual.”
Juventus coach Claudio Ranieri echoed Nedved's words, adding that beating Zenit was never going to be an easy task.
"It was a complicated and very tactical game, as Zenit are in better physical shape than we are and play with five midfielders plus three who move a lot upfront,” said Ranieri.
“We knew they were very good on the counter, so I was pleased we rarely allowed them that chance.
After Wednesday's win, Juventus will be up against newcomers BATE Boris of Belarus on September 30th.