The Dutchman has revealed he was "very unhappy" with his players at half-time on Tuesday evening, before they scored twice in the second half
Ronald Koeman has admitted Southampton were "very bad" in the first half of their 2-0 League Cup victory over Millwall on Tuesday.
The Dutchman's first win in charge was not as straightforward as he might have hoped, with the Championship side enjoying the better of things in the first half at The Den.
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Koeman told Southampton's official website: "The first half was very bad. It looked like the team was playing on 70 per cent and, you know, it's cup football - it doesn't matter the level of opponent, you have to be 100 per cent or you get in trouble. We were in trouble in the first half.
"You can play badly, it's part of the job, but you have to give 100 per cent, and they gave more than we did - you can't accept that.
"We spoke at half-time and I was very unhappy. I'm happy about the reaction in the second half, it was much better, we dominated and we had more chances. We needed to score the second one earlier, but finally we got it."
Koeman also revealed his hope that summer signing Graziano Pelle will be able to kick on from his debut goal for the club.
"It's a great feeling for strikers, they look for goals," the Dutchman added. "Of course they are happy if the team is winning, but if they don't score two or three games in a row then they are a little bit nervous.
"Maybe this gives him the feeling and the confidence that he is a good signing."