The Spaniards are now out of all European competition after suffering a 4-0 defeat at the hands of Shakhtar Donetsk at the Donbass Arena in the UEFA Champions League on Wednesday night.
Goals from Luiz Adriano and Alex Teixeira were capped off by a brilliant brace from Douglas Costa, consigning Arrasate's men to the bottom of Group A with only one point from five games.
Arrasate claimed mistakes cost Sociedad a spot in the Champions League knockout stages and the second-chance option of side-stepping into the UEFA Europa League.
"In this competition, you pay for the mistakes you make," Arrasate said.
"We are sad because this is over. We did not start in a good way."
Real Sociedad's only goal in the group stages of this year's came in their 2-1 loss away to Bayer Leverkusen back in October but Arrasate says his side are determined to go even better and claim a victory over the Germans in San Sebastian on December 10.
"Against Leverkusen, we will play for pride and for our people," Arrasate said.
"We want to do well."
Sociedad currently sit in sixth place in La Liga and Arrasate called on his side to respond with a result when they travel to Espanyol on Saturday.
"It will be difficult, what you need to do is recover well," the 35-year-old said.
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