The embarrassing incident came in Thursday's 4-2 La Liga win for Real at the Coliseum when Casillas charged yards out of area in an attempt to clear the ball only for Parejo to win possession and score what proved one of two consolation goals.
Parejo won the ball cleanly, leaving Casillas clutching his ankle on the turf, and after exchanging passes with Pedro Leon fired a shot through a crowd of defenders into the empty net.
When he went over to check on Casillas, the keeper furiously rejected the gesture and Real coach Manuel Pellegrini said at a post-match news conference Parejo, a former Real player, had been 'disloyal' for not kicking the ball out of play.
However, a calmer Casillas said at a promotional event in Madrid on Friday that Parejo had done nothing wrong.
"When you dedicate yourself to this sport there are some heated moments and yesterday was one of them," he said.
"I have nothing to complain about with regard to Parejo. He did what he had to do and he wasn't at fault at all," he added.
"He took the ball off me cleanly and the rules are clear. A player doesn't have to kick the ball out if the referee is right there on the spot."
