Valencia lost each of their first four league matches this term, but did put their first three points on the board on Wednesday night when Parejo scored a late penalty in a 2-1 win over Alaves.
The Spaniard has insisted that he will continue to 'fight' for Valencia, but has conceded that he "cannot take" any more abuse that occurs off the field.
"I'd be going with my family down the street and they would come up to me and shout 'you're a dog'. I've reached the point where I cannot take this anymore, but that is not a fan of Valencia who does that," Parejo told Cadena Cope.
"I will stick up for the club and for the people until the last day I'm here, fate says that I'm in Valencia and I'm a professional so everyday I'm here I will continue to train and work hard."