The 27-year-old was strongly linked with a move to Sevilla in the January transfer window, but ultimately stayed with Valencia - the club that he has represented since 2011.
"I could have left, but I didn't," Parejo told AS. "I believed it wasn't the best for Valencia because we are in a delicate situation and my duty is to give my contribution to this team to come out of this situation.
"I reiterate that I want my departure to be good for everyone, and in January, it wouldn't have been good for Valencia. There was interest from Sevilla (last summer) - I thought my time at Valencia had come to an end and I told the club that I wanted to leave. The club said no and I stayed.
"We had hoped to compete for Europe but unfortunately, our aim is now to avoid the drop. It has been a mixture of everything. Of course, we, the players, are mostly to blame but we are also affected by what happens around us. We are aware of the situation and united."
A difficult 2016-17 campaign to date has left Valencia in 15th position in La Liga - just four points outside of the relegation zone.