The Southampton manager's plan to beat United focused on their defence.
That victory did not come as a surprise to Dutchman Koeman, though, who clearly had a plan on how to conquer Louis Van Gaal’s Manchester United side, pinpointing the home team’s weakness in defence as a key area to target.
“You know that they have difficulties to build up with three centre-backs,” the Southampton manager said, as quoted by the Guardian.
“The second half we pressed them better than the first. They have a lot of qualities from the midfield to the attack. Fantastic players so you need really good players to stop that.”
Koeman was also keen to highlight the qualities of his own squad, however, pointing out Southampton's excellent record against the so-called big guns in the Premier League.
“If we keep the spirit and the organisation, we can keep in front in the table,” he said.
“We know we have a strong team and that was important in the end of December. We got a point against Chelsea and the three points against Arsenal. That makes belief in the players. It is what you need if you are not a big club: belief in the players, not afraid of the name or the stadium.”
The Saints are now third in the table on 39 points after 21 matches, two more than Van Gaal’s Manchester United side, leaving fans dreaming of potential Champions League qualification.
The Dutchman also thought his side's defensive capabilities were a key aspect of their victory at Old Trafford and of their current run in the league as a whole.
"We defended well and the spirit was unbelievable from the players,” said Koeman.
"Maybe we are [lucky] but if you finally win you deserve to win because I think it's a compliment to the players how they play.”