The Barcelona veteran, who despite returning from a knee injury was an unused substitute during El Clasico, objected to the four minutes of extra time at the end of the second half.
Barca were left frustrated by a lack of additional time following a lengthy break in play to fix the referee's equipment, with Pique the first man to confront Manzano and his officiating team.
"Let me speak! You gave us little extra time, and you've been off the field for a long time," the 34-year-old was overheard telling the official.
Pique's protestations didn't go unanswered with the former Spain international receiving a yellow card for his trouble.
The visitors also felt they should have been awarded a penalty when Martin Braithwaite went down in the box under pressure from Ferland Mendy.
The defeat was Barca's first in 20 league games, a run dating back to early December, and saw them drop to third in LaLiga, a point behind Real Madrid and Atletico Madrid, the latter of whom play their game in hand against Real Betis on Sunday.