Without a single point from their opening three UEFA Champions League group games, Sociedad may have to aim for third spot to continue their continental campaign in the Europa League if they fail to win against their English opponents.
Sociedad are four points behind third-placed Shakhtar Donetsk with Bayer Leverkusen a further two points ahead in second position.
"We know it well, if we don't win tomorrow we will have almost no chance to stay in this competition and will be focused on (Europa League qualification)," Arrrasate said.
"We will prepare well for the game, hopefully being close to our best performance and try to win this match.
"We won't approach the game differently just because there is a possibility we could get eliminated."
Arrasate said he is aware that Manchester United will pose a stern test, but hopes he can upset the form book.
"People are talking a lot about of the period of transition, but the other day, Manchester United also showed the potential they have," he said.
"They are very powerful physically, defending well, coming out on the counter attack very well.
"They might be in a transition period, something expected after being with a coach for more than 20 years.
"I hope we can give them a scare tomorrow."
