Barca had the best chances at Camp Nou, with Lionel Messi hitting the bar and visiting goalkeeper Ondrej Kolar forced into a string of fine saves. However, they were unable to break the Czech side down as they failed to score in a home game for the first time since February 2018.
The local fans grew increasingly unsettled as the match drew on. Ousmane Dembele was whistled when he was taken off on the hour mark and even louder whistles greeted the full-time whistle.
"I would ask for a little patience," Pique told Movistar after the game. "I know the fans want more, we understand that, but we're working hard to find the solutions. Not so much in terms of results, but in terms of how we're playing.
"Everyone has their own opinion. I've spent a lot of time here now and when the supporters expect things to go better and they don't, there is some criticism.
"We [the players] are trying to resolve these situations as quickly as possible. We have to keep cool heads. I think we are in a good position. We're top of La Liga and our Champions League group. We're not playing as well as we expect. The results aren't bad, but they could be better. We do have to improve."
Barca have eight points from their four Champions League games so far. A win from either of their last two games, at home to Borussia Dortmund and away to Inter Milan, will see them reach the last 16.
Asked if the Spanish champions are capable of winning the competition the way they're playing, Pique added: "It's difficult to say right now but there have been times when we've not looked good in the past and we've ended up winning trophies.
"With Luis Enrique, it looked like things weren't working for the first six months and then we won the Treble."
Coach Ernesto Valverde said that "it's good that they're demanding" when asked about the fans' reaction to Tuesday's draw, while defender Clement Lenglet said they're entitled to express their opinions.
"The supporters have the right to express what they feel and we have to accept what they say," the French defender told reporters. "We're going through a difficult moment."
Barca host Celta Vigo in La Liga on Saturday before the next international break. They are sweating on the fitness of Jordi Alba (hamstring) and Sergio Busquets (stomach problem), both of whom were unable to finish the match against Slavia.
Luis Suarez, who sat out the game against the Czechs, is also a doubt with a calf injury.