Lionel Messi's first-half penalty -- his 30th goal in all competitions this season -- was the difference between the two sides at Camp Nou as Barca returned to winning ways after three draws in a row.
Messi missed a second penalty later in the game and Barca squandered a host of chances as they struggled to kill the game off.
Pique said after the match that they must improve immediately as they embark on a difficult run of four away games, starting at Lyon in the Champions League on Tuesday.
"We didn't play well," Pique admitted. "It was not a good performance. We weren't the Barcelona that we want to be.
"The only good news is the win, getting back to winning ways, but we have to improve. The sensations aren't good and we must be better on Tuesday [against Lyon]. If not, things won't go well.
"We have to be more fluid, that's what's given us so many titles. If we don't move the ball quickly, we have possession but we become a weaker team. We know that and other teams know that, so we have to improve."
Pique was one of the few bright points of Barca's performance on Saturday. The centre-back was decisive at both ends, winning the penalty which Messi converted and contributing to a clean sheet in defence.
No one has played more than Pique in La Liga this season -- he hasn't missed a single minute -- but Barca coach Ernesto Valverde played down fears he could suffer burnout in the crucial stage of the season.
"He was great [against Valladolid], as he has been [this season]," Valverde said. "He's looking good, he can cope with the workload. He doesn't play for Spain anymore so he doesn't have that wear and tear. We're really happy with him."
After Tuesday's game against Lyon, Barca face Sevilla in La Liga before two games in a week against Real Madrid, the first in the semifinal of the Copa del Rey and the second in the league.
Valverde believes his players are primed to turn it on in the big games, as Barca continue to fight on three fronts.
"We're ready to hit our best form," he said. "You're not always brilliant in every match and I know we have four important games coming up, but we will just take things step-by-step."