Atalanta scored two second-half goals within four minutes from Josip Ilicic and Robin Gosens to claim the rare away win at Anfield and leave Liverpool to still confirm their qualification for the last 16 of the UEFA Champions League.
Liverpool remains top of Group D with two games to play, sitting two points ahead of both Ajax Amsterdam, who won 3-1 over bottom-placed FC Midtjylland, and Atalanta.
Klopp was criticised post-game for his selection, given they were yet to lock away a last 16 spot, with defensive quartet Neco Williams, Rhys Williams, Joel Matip and Kostas Tsimikas thrust into the XI, along with the returning Mohamed Salah.
“We made five changes; that was very important for us that we did that. In the end, it didn’t work out,” Klopp said.
“That’s part of the deal, you never know before. I would do it again. That was the reason. Five changes means no real rhythm.
“The first half was not a good game at all, they were not good as well. I don’t want to blame them but it was just not a good game.
“Unfortunately, like a second before we could change they scored a goal, the first one, in a space which we knew they try to use.
“We couldn’t defend it in that moment, so they score the first one and then the second one in a similar manner.
“We didn’t create, so that’s it. We had good, better football moments then but not good enough. If you don’t have a shot on target that’s never a good sign.”
Elsewhere in the Champions League on Wednesday, reigning champions Bayern Munich sealed their knockout berth with a 3-1 home win over Salzburg despite being reduced to 10 men.
Atletico Madrid and Lokomotiv Moscow drew 0-0 in the Spanish capital leaving the race for second spot in Group A wide open.
Borussia Moenchengladbach scored a 4-0 home win over Shakhtar Donetsk to firm up their grip on top spot in Group B while Real Madrid continued their resurgence with a 2-0 win at Inter Milan moving them into second.
Manchester City confirmed their passage to the last 16 with a 1-0 victory at Olympiacos, while FC Porto are all but through after a 2-0 win at Olympique Marseille in Group C.