Goals from Joel Ward and Wilfried Zaha ensured it was Crystal Palace who progressed to round four, with Oriol Romeu’s goal not enough for Koeman’s side.
Saints started both halves brightly, but fell behind following a defensive error and were left chasing the game again when Zaha volleyed home with 20 minutes remaining.
“It’s a hard time because maybe it’s the same story every week,” Koeman told youtube.com/southamptonfc
after the defeat to the Eagles.
“I can’t say anything about the teamwork. We tried everything to make the 2-2. Maybe we are a little bit unlucky at the moment, but that’s football.
“We had a lot of things against us and of course if you start well the game, even with a different system, you normally get the first goal.
“We had good moments and controlled the game. One big mistake in our ball possession and we’re 1-0 down. That makes it difficult.
“But we had a good reaction in the first part of the second half.”
Romeu’s goal came after a bright start to the second half, as Koeman highlighted, but the Saints boss was frustrated his side didn’t kick on after equalising.
“What I have to criticise the players for is that we dropped back off, we didn’t continue how we started and that gave them the confidence to come back,” Koeman added.
“They had one more shot on target and it’s 2-1. We did everything after that – we created chances, some good goalkeeper work and two or three shots.
“Then you know it’s the moment with a lot of things against us. We have to continue and show the spirit after the 2-1.
“That’s the way to come back and to be luckier than in the last few weeks.”