The Saints maintained their recent run of good form with a 1-0 win against Sunderland at the Stadium of Light in the Premier League.
Dusan Tadic's penalty in the 69th minute proved to be the difference between the two sides.
Koeman was happy with the final result and has posted the following messages on Twitter:
Back home and 3 points!! pic.twitter.com/TXD8la22JS— Ronald Koeman (@RonaldKoeman) November 7, 2015
Southampton are now seventh in the Premier League table with 20 points from 12 matches.
The Saints are four points behind fourth-place Manchester United and appear to be in the running for a Champions League place.
After the two-week international break, Southampton will take on Stoke City at St. Mary’s Stadium in the Premier League.
Stoke are 12th in the standings at the moment with 16 points from 12 games.