Lionel Messi hit the crossbar in the first half but that was as close as Barca came during a disjointed display that risks dragging Valverde’s team back into the fight for qualification from Group F.
“The other day we lost against Levante and we know this was not one of our best games either,” Valverde said. “We haven’t been convincing either on Saturday or today and we know there is a lot of pressure now on the team. We have to respond.”
Barcelona play Dortmund at home next and will hope progress is secured before their final game against Inter Milan at the San Siro.
The likelihood is they have already done enough to make the last 16 but Valverde will face scrutiny, this blunt performance coming only three days after his side were beaten 3-1 by Levante in La Liga.
If that loss was defined by three goals conceded in seven mad minutes, this one was far less dramatic, a story of stodgy possession in front of their own fans, whose displeasure made for an increasingly sour atmosphere at Camp Nou.
As a dejected Messi stood with his hands on his hips in the centre circle at the final whistle, not even the blast of the stadium music could drown out the whistles.
“In football today and with teams like ours, it is all about winning and winning emphatically,” Valverde said. “It is never enough. The season begins and there isn’t talk of winning a title, there is talk of winning three or four. So the frustration when you don’t win a game is high.”
Slavia’s players saluted their own supporters like they had pulled off a remarkable upset.
– Pique pleads for ‘patience’ –
After all, this was only the third time in 29 Champions League matches that Barcelona have failed to win at home, the other two against Juventus and Tottenham last season, when the Catalans had already qualified.
Their night was made worse by Jordi Alba being forced off at half-time with a hamstring injury while Gerard Pique’s yellow card means he will be suspended for the game against Dortmund.
“I would ask for a little patience,” added Pique. “We are not playing at the level we expect. We have to improve.”
Slavia’s pace in attack caused Barcelona problems in the first 45 minutes, which for the home side was illuminated only by the occasional moment from Messi.
Clement Lenglet almost 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.
Olayinka, Slavia’s gangly forward, was particularly lively as he teed up Lukas Masopust for a shot inside the area before skipping away from Nelson Semedo, who also had to take a yellow card.
Barcelona were sloppy in possession and lacklustre out of it. Ousmane Dembele was erratic and Antoine Griezmann, still playing on the left despite Luis Suarez’s injury, was quiet.
It was up to Messi to lift the mood and he almost scored with a brilliant run from the halfway line that began with a drop of the shoulder and ended with a bending shot against the crossbar.
Both sides had goals ruled out for offside either of half-time, which was greeted by whistles from the home fans, who grew increasingly restless as Barca failed to improve.
They whistled again at Dembele when he was replaced by Ansu Fati and there were groans at mistakes too, like when Semedo headed out for a corner or Lenglet miscontrolled for a throw.
Messi went close but his finish at the near post hit the goalkeeper before Ivan Rakitic, on for Sergio Busquets, curled over late on. When Arturo Vidal stretched but fell short at the far post, the game was up.
