Charlie Austin came off the bench to mark his debut with the winning goal, as Louis van Gaal’s side struggled to break down Koeman’s well-organised outfit.
Having picked up a first win at Old Trafford in 27 years last January, Koeman was delighted to repeat the trick a year on.
“It’s a fantastic feeling for all the players, all the staff and the supporters. Our fans were amazing,” Koeman told youtube.com/southamptonfc
“It’s amazing to win for the second time at Old Trafford. It was well deserved.
“We made it very difficult for them and we know they are a little bit struggling at home and don’t really have the confidence to play and score goals.
“The message to the players was to stay in the game, play out of a good organisation and maybe the second half you can score the goal. That happened.
“I think Man United had one shot on target. That’s fantastic and if you see that, then the win is deserved.”
The victory makes it three wins in a row for Koeman’s side, and he’s pleased with the way momentum is building after a tough run previously.
“It’s sometimes strange to explain why you lose four or five in a row and why now you win three in a row, but that’s football,” Koeman added.
“It’s difficult to understand sometimes, but we need to keep the spirit and our level. Now we have big competition in our squad and I have to make difficult decisions.”