La Real have reached the group stage for the first time since 2003 after knocking out Lyon in the play-off round, while the Ukrainian outfit are making their seventh appearance in eight years.
They may have not featured as regularly as their Group A opponents, Manchester United, Bayer Leverkusen and Shakhtar, but Arrasate is confident in his side's ability to reach the knockout stages.
"We know we're in a group that's difficult but attractive at the same time," he told reporters.
"This game is very important; we're playing at home in what is a short group stage and we want to play a good match. If we play to our level, I am confident we can win.
|13/1||Real Sociedad and Shakhtar Donetsk are 13/1 with PaddyPower to draw 2-2
The two sides have never met in European competition before but Arrasate is well aware of the capabilities of Shakhtar, who helped knock out Chelsea in the group stage last season.
"Their experience in Europe stands out. They're used to competing in the Champions League, they have a lot of quality and they're not afraid to play their game," he observed.
"On the one hand, we have to try to negate their strengths while also playing our game to give ourselves a chance of winning. We've analysed them a lot and we know what we're up against.
"They are team who go out to win games with a defined style of play and they're not going to change. We'll be trying to impose our own style and it should be an open and attractive game."
On the opposing touchline, Shakhtar coach Mircea Lucescu is familiar with Spanish opposition, having faced the likes of Barcelona, Sevilla and Valencia in recent years, but remains guarded ahead of their trip to the Anoeta Stadium.
"Real Sociedad are a good team. Any team that play in the Spanish league as they do and qualify for the Champions League are a difficult team," he remarked.
"They have the same players as last season and they know how to play together. They're a well-structured team, they have top-class players and they're playing at home in front of their supporters.
"They have great players like [Antoine] Griezmann, [Xavi] Prieto, [Haris] Seferovic, [Carlos] Vela and Inigo Martinez and we have to be ready for them."