The south-coast club had to settle for a point at St Mary's Stadium despite playing with a numerical advantage for half an hour following goalkeeper Adrian's red card.
The Spaniard was dismissed after his attempts to wrong-foot Sadio Mane ended with him losing control of the ball and then handling outside the penalty area.
His replacement Jussi Jaaskelainen was given surprisingly little to do as Southampton lacked invention in the final third.
Wednesday's stalemate ensured Southampton dropped a place to fourth after Manchester United beat Burnley 3-1 and Koeman felt his side only had themselves to blame.
The Southampton manager said: "In the final 30 minutes when you play against 10 you have to create more, you have to play more clever than what we did.
"We were a little bit too much in a hurry, we didn't make the pitch really wide and we have to do that. That was the problem in the end.
"I think it’s a big chance, a big opportunity to take the three points and we have, in the last few games, more difficulties to score, to create.
"The front players are struggling a little bit more than before, that was the difference and the reason we didn't win the game.
"You need to be sharp in the box and then maybe you will be a bit lucky, but it was not unlucky. It was really not the best way how we played against 10 men and that was more the problem than luck."
