Arrasate's side have managed only one point and goal from five outings in Europe's elite club competition, with the San Sebastian-based club conceding nine in a tough group that also included English champions Manchester United and Bundesliga side Bayer Leverkusen.
Their focus now switches back to domestic action and Saturday's La Liga game at Espanyol as they try to secure a lucrative place in Europe again for next term.
"In this competition you pay for your mistakes," Arrasate said in an interview with Spanish television broadcaster Canal Plus.
"We are sad that this is over because we were very excited to be taking part," added the 35-year-old, whose side are currently sixth in the La Liga standings.
"We started on the wrong foot especially the opening two matches when I think we deserved more from those games.
"It is going to be very tough to qualify again for this competition. But I think we are playing well in La Liga and improving all the time.
"What we have to do now is recover well and focus on Saturday's game."
Sociedad have one more Champions League game to play when they host Leverkusen, who still have a chance of making it through to the last 16, on December 10.
Arrasate said he and the players were determined to put on a good show for the home supporters.
"We have a sixth match left now when we theoretically will not be playing for anything," Arrasate said.
"But with everything the Champions League represents I think we owe it to the fans to make an effort to win the last game.
"We would have like to have done better but it wasn't to be and now we have to think about Saturday's La Liga match."
(Reporting by Iain Rogers, editing by Patrick Johnston)
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