Goals from Marcus Rashford and Ferran Torres secured Barcelona's triumph and extended their lead at the top of the table to 14 points with only three matches remaining, condemning Madrid to a second straight season without a major trophy.
Arbeloa, who replaced Xabi Alonso midway through the campaign, acknowledged the disappointment surrounding the club's season and said the players had fallen short in key moments.
"We need to take a step forward collectively and have a much clearer idea of what we want to do," Arbeloa told reporters after the defeat.
"We have to put the collective ahead of the individual because talent alone is not enough. We dropped too many points in games we should have won."
Madrid's campaign has been marked by inconsistency despite the arrival of superstar forward Kylian Mbappe ahead of the season. Questions have persisted over the balance of the side when Mbappe, Vinicius Junior and Jude Bellingham play together.
Mbappe missed the Clasico with a thigh injury, while criticism intensified after the France captain travelled to Sardinia during his recovery period. Arbeloa, however, refused to criticise the striker.
"What I would have liked is for him to be 100 percent and able to play," he said.
The defeat also capped a turbulent period for Madrid, who exited the Champions League in the quarter-finals and have dealt with internal tensions, including reports of a dressing-room altercation involving captain Federico Valverde and Aurelien Tchouameni.
Despite the setbacks, Arbeloa insisted the squad remains strong enough to compete at the highest level.
"We have a great squad and many clubs in Europe would want these players," he said. "It hasn't been easy with the injuries we've had to important players, but the club will always look to improve."
The Madrid coach also urged his players to finish the campaign professionally despite the title race being over.
"We are defending something bigger than ourselves, which is the Real Madrid badge," Arbeloa said. "We have to finish the season strongly and try to win the remaining matches."
Arbeloa's own future remains uncertain, with former coach Jose Mourinho reportedly linked with a return to the Bernabeu. The Spaniard said discussions with the club would take place once the season concludes.
"We'll have a conversation with the club, as is normal," Arbeloa said. "Right now my focus is on helping the team finish the season in the best possible way."
