The Saints boss was delighted with the spirit shown by his side - and his goalkeeper in particular.
The Saints held on to a 0-0 scoreline for as long as they could but were undone by a late Alexis Sanchez winner when they were down to 10 men through injury.
Koeman, however, was delighted with his side's response to losing 3-0 to Manchester City on Sunday afternoon.
And the Dutchman singled goalkeeper Fraser Forster out for praise, in particular.
As Opta stats show, the Southampton boss was not wrong...
|Brad Guzan||Aston Villa||5|
The 26-year-old made more saves against Arsenal than any other goalkeeper has done in the Premier League this week.
The Saints now face Manchester United next, completing a trio of extremely difficult fixtures for Koeman's side.
If they can show the same spirit they did at Arsenal, however, they should fare considerably better against the red half of Manchester than they did against the blue.