Sociedad welcome the Catalan powerhouse to the Estadio Municipal de Anoeta on Wednesday, after Barca were 2-0 winners at the Camp Nou in the first leg.
Arrasate, though, is empowering his players to believe in reaching the cup final, where they would meet Real Madrid.
"I'm the first to believe we can do it, while I am aware of how difficult it will be," he said.
"At the moment, we still have a chance and the first step we must take to realize that dream is to believe we can do it.
"The players also have faith that we can beat Barca, I hope we can witness a magical night at Anoeta tomorrow."
Arrasate did concede it would take an almighty effort to unseat the Spanish champions.
"To mount a comeback, we need determination, belief, courage, faith and hope. We are going to need all of that and more," he said.
Sociedad were forced to play with 10 men for more than half of the first leg but Arrasate was hoping to channel their anger into positive energy.
"The players are still very angry about what happened, we need to harness that anger and use it positively," he said.
"In the cup, anything is possible but we have to go out and look for it, it won't come to us easily."
Arrasate said his side would practice penalties, and said he would gladly take a 2-0 result after 120 minutes.
"That's something we do very often when we have a cup tie," Arrasate said of their penalty practice.
"We did it when we met Algeciras, Villarreal and Racing. We'll be practising penalties but without giving it too much importance although right now, we'd quite happily accept a 2-0 win and for the tie to be decided with a shoot-out."
