The 25-year-old, whose contract expires at the end of next season, used the social media site to voice his displeasure at the sale of Andy Carrol and Kevin Nolan.
"The club is allowing all the major players of the team to go," Enrique tweeted. "Seriously, do you think it is the fault of the players? Andy [Carroll], nobby [Kevin Nolan] etc etc. This club will never again fight to be among the top six again with this policy."
While Pardew admitted that he was disappointed at the comments, he insisted that the player is still welcome at the club.
"Jose was wrong to put those comments up and I told him," Pardew told The Sun.
"It's a good offer which we have given him and maybe the frustration of the situation got the better of him.
"I want him to stay, he's a good lad but this didn't reflect well on him. It was a mistake, he knows it and so do I."
Enrique has been linked with a move away from Newcastle, with Liverpool and Arsenal said to be interested in the former Villareal defender.