Cornella is a suburb of Barcelona, where the club's Cornella-El Prat stadium is based, and Pique's implication was that Espanyol do not deserve to be considered Barca's rivals.
Gerard Moreno put the hosts ahead midway through the second half and Pique equalized with an 82nd-minute header in a heated match at RCDE Stadium.
The opener came after Espanyol had a goal disallowed in the 47th minute after Leo Baptistao was judged to have run the ball out of play before cutting it back to Esteban Granero who found the net.
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The defender was referring to the area of Barcelona where the club have played their home games since 2009 in an attempt, Espanyol believe, to discredit them. I know it hurt them and I used sarcasm to annoy them but saying they play in Cornella is not disrespectful, it's a fact.
"It means we're on a good run, although with regards to how I feel right now it doesn't tell me anything".
"Some of the fans here have been directing insults at me and my family for a long time".
"They complain about that and report me, but they don't investigate insults towards my family".
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La Liga topscorer Lionel Messi has been named among the substitutes for Barcelona's derby game at Espanyol on Sunday, the first time the Argentina superstar has not started a LaLiga game this season.
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.
Ernesto Valverde's men have otherwise proved to be exceptionally resilient, so it was perhaps unsurprising they were able to turn around the tie.
In torrid conditions, with the rain pouring down throughout the 90 minutes and puddles forming all over the pitch, Barcelona looked set to see their unbeaten league record taken by Espanyol, who had ended their 29-game unbeaten streak in all competitions last month.
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"It was one of the most exciting games", coach Quique Sanchez Flores said. "We are working to get better results and to improve".