Saints wasted a good chance of reaching the final at Wembley as they suffered a shock 1-0 defeat at the quarter-final stage to League One side Sheffield United.
It was Koeman's first season in England and, with hindsight, the Dutchman admits that perhaps his team were not as prepared as they should have been playing against lower-league opposition away from home.
There were no such oversights on Wednesday night as Southampton thrashed MK Dons of the Sky Bet Championship 6-0 to once more make it through to round four - where they will host Aston Villa.
Jay Rodriguez, Sadio Mane and Shane Long all scored twice as Saints humiliated the Milton Keynes club, inflicting the biggest defeat of their short history a nd Koeman has his sights set on going at least one step further in the competition than last season
He said: "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
"It was always important to win because we like to be strong and we like to win games and we like to do well
"We had a run last year to the quarter-finals and we will try to get further on in this tournament, and that ambition we showed
"We (will) take it seriously and of course we change some positions, but we have more competition in our squad than we had last year
"We like to win and we try to win everything
It's a title and we will fight for it."
Ryan Bertrand, fit again after knee surgery, came on for his first Southampton appearance of the season in the 55th minute in Milton Keynes
Koeman added: " I am very pleased because he is a very good player
He did a great job in all the games he played last season
"But Ryan is close to being back
Last week he played 45 minutes for the under-21s and now 30-35 minutes and we are getting him back to his best physical level."
Despite the ignominy of overseeing the club's heaviest ever defeat, Dons boss Karl Robinson was philosophical on reflection of the night's events
"We're a bit embarrassed and upset, obviously
But their team is worth about Â£98million, to my two hundred grand..
I don't think Houdini could've got a result," said Robinson.
"But forget money and the talent that can buy, Southampton's hunger and desire was absolutely phenomenal."
Source : PA