Jay Rodriguez, Sadio Mane and Shane Long all netted twice as Saints humiliated the Milton Keynes club, inflicting the biggest defeat of their short history
Rodriguez's goals were his first domestically in almost 18 months, having only recently returned from a lengthy lay-off with a ruptured anterior cruciate ligament
He netted for the first time since his comeback against Danish outfit Midtjylland in the Europa League last month but his efforts on Wednesday night were his first strikes in English competition since a Premier League double against Newcastle on March 29, 2014.
The 26-year-old's brace, his second from the penalty spot, came either side of Mane's double while Long grabbed his two later in the second half.
Koeman said: " The final result is very pleasing and I think we showed from the first minute to the last second the great spirit in the team
''We had a good start and two fast goals gave us the confidence and total domination in the game but after half-time the message to the players was to continue what we did in the first half and try to score more goals and keep a clean sheet.
''I am very pleased because usually in this competition the results are close, it is usually 1-0 or 2-1.''
All of Koeman's strikers got their names on the score-sheet but the Dutchman did not want to single out any specific players for praise.
"The whole team worked well - the defenders, the midfielder and the strikers
They all had the right spirit, so it is not fair to pick people out, but goals do strikers good so that is pleasing also."
MK Dons boss Karl Robinson admitted he was in awe of Saints at times
''That is a team who wants to win the competition, their hunger and desire was phenomenal,'' said Robinson
''I found myself applauding some of their football at times.
"In my time working at that level at Liverpool and Blackburn that was as cohesive a display as I have ever seen.
"We are a little embarrassed and upset, I admit
But they are a very good side and hopefully me and my players can learn something from this game."
Source : PA