Koeman is under pressure to keep his job at Goodison Park, with the Toffees only sitting in 16th place in the Premier League table and facing an uphill struggle to qualify for the Europa League knockout stages after losing to Lyon on Thursday night.
However, Koeman has insisted that he is taking confidence from his team's performances against higher-profile teams last season, despite having already suffered defeats to Chelsea, Tottenham Hotspur and Manchester United since the start of this campaign.
The 54-year-old told reporters: "If you look back to last season, we had good games at home against big teams in the Premier League.
"Arsenal aren't unbeatable and haven't been that strong away from home. We need to improve and play better. If we bring fight and aggression in a good way we have a good chance."
Everton have registered just four points from their last six fixtures in the top flight.