The Saints were beaten 6-1 in the Capital One Cup on Wednesday evening.
The Saints were hammered 6-1 by the Reds in the Capital One Cup, with them falling apart in the second half of the game.
They were already 3-1 down at that point, but a switch to three at the back by Koeman saw them allow Liverpool to run riot and secure an impressive win.
And the Dutchman took complete blame for the second half, but says it was defensive mistakes that truly cost them in their quarterfinal clash.
“If you make the mistakes defensively we did in the first half and the top quality of Liverpool, then you can lose,” he told Sky Sports.
"The second half is my responsibility. I changed the system, I made the risk of three at the back.”
“They have a great energy and they have qualities in the team. We gave them that space, those opportunities and if you give a man like Daniel Sturridge that space he will kill you."
With them now out of the cup, the Saints must turn their attention back to the league, with a place in Europe very much up for grabs.
They current sit tenth on the table on 20 points, just three points behind Liverpool, who currently occupy the last Europa League place in sixth.
They have not been in the best of form of late though, with the loss to Liverpool the latest of several disappointing displays.
However, this weekend they take on Aston Villa, who are currently bottom of the table, meaning a return to winning ways is very much expected.