Champions City replaced Southampton in second place in the Premier League with a convincing 3-0 win at St Mary's Stadium on Sunday - a result that represented just a third loss of the season for the hosts.
Koeman's superb start to life on the south coast means his side still enjoy a four-point cushion in third spot over Manchester United, and they can visit the Emirates Stadium full of confidence having already won there in the League Cup back in September.
Wednesday's game comes in the middle of a challenging eight-day period for Southampton, which culminates with a home match against United next Monday.
But while Koeman - who will be without Morgan Schneiderlin (thigh) at Arsenal - admitted his players are somewhat downbeat after Sunday, he wants their trip to north London to be seen as an opportunity.
"Of course, it's been different. The faces are different when you lose, that's normal," the Dutchman told his pre-match media conference on Monday.
"It has to be like that because if you don't have that you don't learn.
"We know on Wednesday we play again and there is no time to be disappointed with one result.
"Arsenal is the best way to have a good reaction - that means working hard and showing it on the pitch.
"Like City, they had some problems but the spirit of them is back and they have good players - they are a team who has to fight to win the title or there are critics."
While Koeman's side were comprehensively beaten at the weekend, Arsene Wenger's Arsenal bounced back from successive Premier League losses to Swansea and United by winning 1-0 at West Brom.
However, Wenger's hopes of closing the gap to one of their rivals for a European berth have been dealt a blow with doubts over Nacho Monreal, Kieran Gibbs and Alex Oxlade-Chamberlain due to knocks.
Nevertheless, the Frenchman remains upbeat, despite murmurings of discontent regarding his tenure from sections of the Arsenal support.
"We can let people talk," Wenger said.
"We live in a society of total opinion but we live off not what we say but what we do and what we do is on the football pitch.
"It is the responsibility of everyone at the football club to prepare the future always."
