Pique's gesture came after Espanyol reported the defender to the Royal Spanish Football Federation for referring to them as "Espanyol from Cornella" following the teams' Copa del Rey tie last month.
The former Liverpool star hit the bar in the first half before Gerard Moreno's header gave the hosts the lead midway through the second.
Barcelona fought hard to get back into the match after going behind and managed to find an equaliser seven minutes from time when Gerard Pique rose highest to head home a pin-point cross from Lionel Messi, 1-1.
Barcelona's Luis Suarez curled a free-kick narrowly over, although Espanyol thought they had scored in the first minute of the second half when the ball had gone out before Baptistao cut back for Esteban Granero to convert.
Cornella is a suburb of Barcelona, where the Cornella-El Prat stadium has been Espanyol's home since 2009, with Pique's implication being the club do not deserve to be considered Barca's rivals.
"Celebrating the goal was special after everything that's happened in the last week", Pique told reporters after the game.
"Some of the fans here have been directing insults at me and my family for a long while".
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"That doesn't mean anything to me right now, but it's a good statistic", Valverde said. Maybe it should have been directed at the club or its owners for not reporting certain things.
While they were last in the Segunda Division in 1994, now spending their 24 consecutive season in the top flight, Espanyol have yet to make a name for themselves, aside from being Barca's noisy neighbours.
"They complain about that and report me, but they don't investigate insults towards my family".
Fixtures between the two are often one-sided, with Barcelona winning all-but one of their last five matches, scoring 14 goals in the process, compared to Espanyol's two solitary strikes. Thomas Vermaelen and Andre Gomes are still doubts for the weekend for Ernesto Valverde's side.
Up ahead in midfield, we might see Valverde hand a rest to captain Andres Iniesta, with the veteran midfielder playing every single game lately.
"We have to repeat what we did in the cup match where we defended very well and didn't allow them many chances".