The Andalusians drew their first two Champions League games against Lens and PSV Eindhoven, leaving them little leeway for further mistakes if they are to progress from Group B.
Uruguayan coach Alonso replaced Jose Luis Mendilibar earlier in October with the team struggling both in La Liga and in Europe.
"What I think is that we have a great opportunity," Alonso told a news conference Monday.
"I'm optimistic, naturally - where many people see obstacles, I see an opportunity.
"Tomorrow we have a great opportunity to fight for the three points."
Alonso's first game was a baptism of fire against Real Madrid on Saturday at the Ramon Sanchez-Pizjuan, which he passed with a 1-1 draw in La Liga.
Sevilla showed more grit than expected after a weak start to the season, just as Alonso had asked of them before the game.
Sergio Ramos defended superbly in the draw against his former side and appears vital to Alonso's set-up, after reports he was not enjoying his football under Mendilibar.
The coach said it was a pleasure to have the veteran in the team and there were no problems with managing a dressing room stacked with leaders.
"Sergio is a very important player for the club and evidently, he's at the same level of importance as Jesus (Navas), Ivan (Rakitic) and Fernando, those four are the leaders of the dressing room," continued Alonso.
"Despite what people think, having four players of such status makes things a lot simpler for me, it makes my job easier."
Alonso said the record seven-time Europa League winners need to play at their very best to get a result against Mikel Arteta's side, joint top of the Premier League with Manchester City.
"They know what they want, they are very good, truthfully, but we have to fight all over the pitch, we have to give absolutely everything to enjoy ourselves," added Alonso.
"We have to work for 90 minutes or more, very hard in all areas.
"I think the team is ready, they can do it, they have the quality, they have the leadership."
Sevilla, third in Group B, trail leaders Lens by two points and are one point behind the Gunners, second.
Former Tottenham winger Erik Lamela said facing his former rivals again with Sevilla would be a "special" occasion.
"I want to win, a player always wants to win when they go on a football pitch," said Lamela.
"That I played for Tottenham means something to me, and this game is special, yes."
