The loss handed Barcelona their 29th LaLiga crown with three matches to go and condemned Real to a trophyless campaign, capping a miserable year in which Xabi Alonso was sacked midway through the season and Arbeloa failed to halt the slide.
"There isn't much we can say; we understand their frustration, their disappointment, and just how dissatisfied they must be with this season, all we can do is work hard and look to the future, learn from everything we've got wrong this year," Arbeloa told reporters.
"Real Madrid always bounce back, we've fallen many times and got back up many times, but I understand the anger any Real Madrid fan might feel; we have to work to turn the situation around."
Madrid's campaign unravelled on several fronts, including a Champions League quarter-final exit against Bayern Munich, while tensions rose further on Thursday when captain Federico Valverde went to hospital after a changing-room fight with teammate Aurelien Tchouameni.
Arbeloa said there could be no easing off despite the title race being over, urging his players to be professional and honour the badge in the final three games left in their schedule.
"With even greater responsibility, knowing that our season is over, we cannot let ourselves down; far from it, we have to go out there to win," Arbeloa said.
"We are defending something greater than ourselves, which is the Real Madrid badge. We have to play three great matches and secure three great victories."
Asked whether Madrid needed a rebuild, he backed his players.
"We have a great squad; we can get a lot out of them. It hasn't been easy at all with everything that's happened over the last few months – many key players out. The club will always look to improve, but we have a squad of very good players that any team in Europe would want," Arbeloa said.
On his own future, Arbeloa said discussions would come later.
"As you know, we'll likely have a conversation with the club. What I want is for the team to finish the season strongly, for the players to get some playing time – that's my goal. As for what the future holds, we'll have to wait and see," Arbeloa said.