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 an entire half with just 10 men
First-half goals from Thulani Serero and Danny Hoesen allowed 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 restart, Frank de Boer's men held on to claim a vital win.
Pique, who started at centre-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 they are to win anything this season.
"We played a horrible first half," the former Manchester United man, 26, 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 are no longer unbeaten, they can take some solace from the fact that they remain top of Group H ahead of their final match of the round against Celtic, who are doomed to finish fourth, while Ajax and AC Milan will battle it out for second place at San Siro.