The Reds went into the break facing a one-goal deficit, after Swans midfielder Leroy Fer touched the ball home from point-blank range.
Both Milner and Jordan Henderson revealed the manager had some strong words for his players at half-time, and Klopp elaborated on this during his post-match press conference at the Liberty Stadium.
“I said [to them] I’m 49, I’ve lost a lot of football games and I will lose a few [more]. But it didn’t make sense to lose [today],” he said.
“We were angry at half-time, but with ourselves. We had to show we could do better.
“It was very important we showed the reaction in the second half.
“I didn’t think this would be the day that we would be that bad.”
With six days to prepare between last weekend’s 5-1 victory at home to Hull City and the trip to south Wales, Klopp said he saw nothing on the training ground that suggested Liverpool would struggle.
However, continuing his overview of the Reds’ first-half performance, he lamented that they “weren’t ready.”
“It was bad. We weren’t ready for this game. It’s my responsibility we’re ready, and we weren’t,” he added.
“It was too static. Swansea did well, but we were really too static. It’s not allowed to be that easy.
“We were never compact enough for counter-pressing.”
Their performance after the interval was more in line with their impressive displays from the season so far.
And it was clear that Liverpool required Klopp’s intervention to inspire them to fight back for their fifth league win of the season.