The two clashed after a fiery encounter on Sunday in which Real's Cristiano Ronaldo had to be taken off after suffering an eye injury which restricted his sight.
"All of our players and coaching staff behaved in an exemplary fashion during the course of a match which took place in conditions which made playing football very difficult and which our team was able to overcome in a professional, dedicated and sporting manner," Real said on their website (www.realmadrid.com).
"At the end of the match the attitude and behaviour of the players, coaching staff and members of the expedition was at all times correct and beyond reproach," the club added.
"We reject the accusations in some sections of the media regarding supposed provocations by our player Pepe towards the home team's dressing room.
"Our player's behaviour was at all times exemplary, like that of the rest of his team mates.
"This club will continue to defend at all times the values of sporting behaviour and respect that should guide the world of sport."
In response, Levante issued a statement which mimicked the wording of Real's almost to the word. It is unclear whether the two teams will be charged.