Madrid's lead at the top of La Liga has been cut to six points over defending champions Barcelona after a tricky week which started by conceding an injury-time equaliser to Malaga at the Bernabeu and continued with a stormy 1-1 draw at Villarreal.
Cristiano Ronaldo put the visitors ahead at El Madrigal before they imploded, with Sergio Ramos and Mesut Ozil both sent off, along with coach Jose Mourinho and fitness coach Rui Faria.
Defender Pepe could also face disciplinary action from the Spanish federation for directing abuse at referee Paradas Romero in the tunnel after the game.
Mourinho and his assistant Aitor Karanka refused to speak to the media afterwards and have cancelled Friday's scheduled press commitments over what they perceive to be victimisation.
Pardeza did raise his head above the parapet, however, and insisted the club will battle through the controversy and win the league.
"We will continue to fight for our goals because we are still in an enviable situation," he told Marca.
"We will continue with the same spirit and attitude. Nothing and nobody is going to give up.
"The club would like to reassure the staff that our wish is to fight under the same conditions as others.
"That's what we want, to play on an equal basis."
Although Barca have cranked up the pressure by winning their last six La Liga games, Pardeza believes Mourinho's men can prevail.
"The strength and mental toughness of this team is unquestionable and the Madrid fans should not worry because this is a squad with tremendous character," he added.
Sociedad have been dragged back towards the relegation spots in recent weeks after a run of three defeats in four games, the latest of which came on Wednesday when Levante left San Sebastian with a 3-1 victory.
And defender Mikel Gonzalez is hoping Saturday's match official Turienzo Alvarez is not swayed by this week's high-profile incidents.
He said at a press conference: "I hope he is not influenced.
"We know the impact of everything that happens around Real Madrid and Barcelona. They can fill an entire newspaper putting pressure on referees.
"But the refs are professionals and they know what is at stake for others. Not only are Madrid playing for things, so are we."
Gonzalez admits the midweek setback was disappointing.
"We lost against Levante which was an important opportunity to move away from the places below and it is true that it may cost us.
"Now we have to try to obtain a positive result in the Bernabeu.
"They have some important players out as do we, but obviously we are playing one of the best teams in the world and we will have to concentrate until the final minute of the match."
Sociedad will be missing Dani Estrada and Gorka Elustondo through suspension but Antoine Griezmann returns.
Ramos and Ozil are unavailable for Madrid due to their midweek misdemeanours while Lassana Diarra is also suspended for an accumulation of yellow cards.