Questions surrounding the altercation between midfielders Federico Valverde and Aurelien Tchouameni dominated Arbeloa’s news conference on Saturday.
The incident left Valverde ruled out of El Clasico because of concussion symptoms, while both players were fined 500,000 euros (£432,000) following a club investigation.
Tchouameni returned to training on Friday and remains available for the match, although Arbeloa declined to confirm whether the France international would start.
“The players have acknowledged their mistake, expressed their regret and asked for forgiveness. That’s enough for me,” Arbeloa told reporters.
“These two players deserve for us to turn the page and allow them to keep fighting for this club. I’m very proud of them. I won’t allow this to be used to question their professionalism.”
Former Liverpool, Real Madrid and Spain defender Arbeloa also suggested dressing-room disputes were not unusual in elite football environments.
“I’ve had a team-mate who picked up a golf club and swung it at another player,” the 43-year-old said.
“What happens in the Real Madrid dressing room should stay in the Real Madrid dressing room, and that’s what hurts me the most.”
Arbeloa was referring to an incident during his time at Liverpool in 2007, when a disagreement between Craig Bellamy and John Arne Riise during a training camp in Portugal reportedly escalated into Bellamy confronting his team-mate with a golf club.
“These are situations that have always happened, although I’m certainly not justifying it,” Arbeloa added.
“It was an incident and we were unfortunate that Fede ended up with a gash. It was more bad luck than anything else.”
The Madrid coach also accepted responsibility for the situation.
“If you want to blame someone, here I am,” he said.
Despite the controversy, Arbeloa insisted the focus remained on Sunday’s meeting with Barcelona.
“We face the Clasico with the ambition to do things well and go to win.”
Arbeloa does not appear to have a long-term future in his current post, with reports in Spain already linking several high-profile names, including Jose Mourinho, to the role for next season.
Pressure has also intensified on club president Florentino Perez, with questions being raised over a period that has seen Real Madrid go through three managers in two campaigns without lifting a trophy.
The club’s next appointment is now viewed as one of the most significant decisions of Perez’s presidency, as Madrid attempt to restore stability and competitiveness after a turbulent season on and off the pitch.
Despite the scrutiny, Arbeloa strongly defended the 79-year-old president.
“There is no-one more prepared than Florentino Perez to turn this situation around,” he said.
“I remember how the club was before his arrival. He is the president with the most titles in Real Madrid history and he brought the club back to where it belongs. We all have to fight together.”