"That was a good lesson, that if you are not really 100 percent prepared for the game, you can get problems against everybody," he told the club website (www.saintsfc.co.uk).
"I've said always winning games brings confidence .... The most comfortable situation is to win the game because that gives really a good confidence for Saturday (against Swansea City in the Premier League)."
The Dutchman also said Southampton had to be ready for MK Dons to come at them with a 'nothing to lose' attitude.
"I expect a tough game because for them it's a great opportunity to play a Premier League team," he said.
"We need to be prepared because in this kind of competition it's not about the level you play against, because they fight for their lives in these kind of matches."
Ideally Koeman would like to rest some players for the Premier League campaign but was wary of underestimating MK Dons, who are 20th in the 24-team Championship.
"Maybe they are a little bit more struggling in the league until now from the start, but it's a strong team," he said.
"I would like to go on in this tournament and to put a strong team out to beat them.
"One or two changes more maybe than we did last year, but that's all about the competition that we have in the squad. Everybody is working hard to get the chance to play," Koeman added.
(Reporting by Simon Jennings in Bengaluru; Editing by Peter Rutherford)
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