The visitors' goalkeeper Adrian was given his marching orders with 30 minutes of the game remaining after he handled outside his penalty area following pressure from Southampton forward Sadio Mane.
Despite dominating the remainder of the game against 10 men the hosts could not find a breakthrough and the draw meant they slipped one place down to fourth after Manchester United lbeat Burnley 3-1.
"If you play 30 minutes 11 against 10 then you have to score the goal but we didn't," Koeman told reporters. "Everybody was running and we didn't make the pitch wide to make the space. There were too many crosses and I think that is the easy way for them to defend.
"I think we had one or two shots from outside the box and lacked sharpness up front. I said at halftime if we kept the organisation, the front players have to win the game tonight but they didn't."
It was the lack of cutting edge from his high-flying team, who have exceeded all expectations, that frustrated Koeman the most.
The Dutchman singled out striker Graziano Pelle for criticism after the Italy striker headed wide in stoppage time to make it eight league games without a goal.
"You have to react and work harder and be sharp in the box," Koeman said. "Maybe in one or two situations Graziano Pelle was a little bit unlucky but he was not on the level he can bring."
Southampton are still in fourth place, the final Champions League qualification spot, with 46 points and 13 games remaining. They host Liverpool next in the league on Feb. 22.
(Reporting by Sam Holden, editing by Ed Osmond)
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