The defender was highly critical of the Blaugrana after they were beaten for the first time this season, succumbing to a side that had to play much of the match with 10 men.
First-half goals from Thulani Serero and Danny Hoesen deservedly put the Dutch in complete control and, although the Blaugrana threatened a comeback when Xavi scored from the penalty spot following Joel Veltman's red card just after the break, Frank de Boer's men held on to claim a vital win.
Pique, who started at center back alongside Javier Mascherano, with Carles Puyol at left back, was enraged by the end of Barca's 20-game unbeaten run and insisted that the squad cannot afford a repeat performance if it is to win anything this season.
"We played a horrible first half," the former Manchester United man told reporters after the match. "There is no excuse - it was a disaster. What happened in the first half can't happen again. The attitude wasn't right; the whole team know that."
Although Barca is no longer unbeaten, it can take some solace from the fact that it remains on top of Group H ahead of its final match of the round against Celtic, which is doomed to finish fourth, while Ajax and AC Milan will battle it out for second place at San Siro.