The Reds came from two goals down at Anfield twice to win 5-4 on spot-kicks in the Carabao Cup quarter-final.
Jamie Vardy netted twice inside 13 minutes to put City in front but Alex Oxlade-Chamberlain pulled one back for the hosts in a breathless opening 20 minutes on Merseyside.
James Maddison blasted home from range to restore Brendan Rodgers’ City back to a two-goal lead.
However Diogo Jota slotted home after half-time and Takumi Minamino equalised five minutes into injury time to send the game to penalties.
Luke Thomas and Ryan Bertrand fluffed their lines from 12 yards, allowing Jota to step up and win the shoot-out in front of the 5,000 travelling supporters.
Klopp spoke about City’s formation, a diamond because of a lack of wingers available to Rodgers, and the goals as well.
The German made half-time alterations to bring his side back into the game.
“First half, always when we played football we were good,” said Klopp.
“When we played the right football we were good. When we played exactly in their formation, then it was not that good and then they won their balls easily and then they had their counter-attacks and scored easy goals.
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“OK, the first two; Maddison was obviously… We lost the ball before that as well in a not very comfortable moment and he could use his shooting skills.
“But at half-time I told the boys I actually liked the game apart from the mistakes we made around the goals and we have to improve and do better in a few moments.
“We should not play in their formation, we have to use their formation to play around, to play next to the six, to switch more often to accelerate then, and to play in the half-spaces.”