Spanish media reported that Real defender Pepe and Levante captain Sergio Ballesteros had been involved in a confrontation near the dressing rooms and the referee referred in his match report to a clash between an official from each club that had to be broken up by security staff.
Real won the game, which was played in atrocious conditions on a heavily waterlogged pitch, 2-1 after playing the second half without top scorer Cristiano Ronaldo.
The Portuguese was struck in the face by David Navarro's elbow early in the match and the blow opened a gash below his left eye and caused problems with his vision.
"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.
"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."
Real published their statement at around 5pm. local time and Levante responded with a heavy dose of irony some four hours later.
The Valencia-based club's statement used almost exactly the same wording as Real's, also referring to the "exemplary behaviour" of their players and officials, and only the final part was altered.
"We would like to highlight the performance of our players and technical staff during yesterday's spectacular match, for their dedication, fight and competitiveness," Levante said.
"We would also like to express our gratitude for the unconditional support of the fans who were cheering on the team the whole game despite the rain," they added.
"Levante will continue with its philosophy of defending the values that have made our 100-year-old club loved and respected by Spanish football."
It remains to be seen whether the Spanish football federation's disciplinary committee, which typically takes action only on incidents that appear in the referee's match report, will sanction the two clubs.
