Southampton have been keen to learn from their Capital One Cup defeat to Sheffield United last season.
The Saints had a brilliant 2014/15 campaign, but their defeat to League One side Sheffield United in the Capital One Cup quarter-final was one notable disappointment.
Now, after a 6-0 win against Milton Keynes Dons in the same competition, Koeman says that his side have heeded the lesson that they were given last season, and they are stronger for it.
"Last season was a good lesson, that if you are not really 100 per cent prepared for the game, you can get problems against everybody," said Koeman.
"It was always important to win because we like to be strong and we like to win games and we like to do well."
Southampton brushed aside the Dons, putting in a performance which showcased their ruthless streak and attacking intent.
Sadio Mane, Jay Rodriguez and Shane Long all got on the scoresheet twice during the fixture, with the Saints running riot at stadium:mk.
It was a display which they will hope kick-starts their season, as Koeman's side have opened the campaign well short of their best.
Southampton have won just one of their opening six Premier League games, and they will be keen to get back on track by beating Swansea City on Saturday.