Lionel Messi almost won the game for the Spanish side with an unbelievable solo run in the first half as he went from midfield all the way to the top of the box, firing a lovely shot off the crossbar.
It was the first time in seven years that the Catalan club have failed to score at home in a European group stage game with Gerard Piqué admitting afterwards that his side were left "surprised" by some aspects of Slavia's play.
But Valverde's side, who struck the woodwork through Lionel Messi, were unable to break down the Czech champions in a game which saw both sides have goals disallowed for offside.
"They, without creating clear opportunities, caused danger when they stole the ball from us because they came out very fast against us (on the counter attack)".More news: Veterans Day events, deals in Tampa Bay
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Barca have eight points from their four Champions League games so far.
"I would ask for a little patience", added Pique. We're top of La Liga and our Champions League group.
Clement Lenglet nearly conceded an early penalty when Marc-Andre ter Stegen pushed a pull-back into the defender's chest while Pique accepted his booking after being robbed of the ball by Peter Olayinka.
"We're the first team in a long time to keep a clean sheet here, everyone knows that Barcelona is a goal factory".
"We'll try and sort things out, to improve, but it's time for a cold-blooded, calm-headed analysis. I felt like we could have won".
"We don't have any time to sit around and get anxious, we have to keep working and play every three days".