The Reds were below their best against the Serie A side in their second fixture of Champions League Group C and were punished in the final minute when Lorenzo Insigne tapped in Jose Callejon's cross to take the points.
Naby Keïta was taken to hospital after being carried off the field on a stretcher suffering from severe pain in his back during the first half of Liverpool's 1-0 Champions League defeat.
The Guinea global is set to travel back to Merseyside with his team-mates but is unlikely to be risked when Liverpool face Manchester City on Sunday.
"That's the second time this season that we have conceded a goal like that, then they were on their bikes, the atmosphere was there because we let them do what they did".
"If you looked how we played you would have thought they were always on us - we could have played calmer but we didn't".
Ancelotti said, "The team did well throughout the game, we never lost control, were always very focused, above all when defending and allowed Liverpool practically nothing". We weren't as good as we could be. They had a good game, we didn't, that's what they deserved the three points. They deserved to win.
Speaking after the game, Klopp explained that he would "have to wait" to learn the extent of the injury, confirming in his post-match press conference that it was a back problem.
"And you have seen it has been absolutely intense since the last global break with the games we've had - twice Chelsea and stuff like that, coming to Napoli, playing PSG and now we have the game on Sunday against Man City".
"I think we interpreted the game really well, we changed a bit - but not too much - the way we played with an extra central defender", said the Italian. But this was a reality check on how things must not go.
"We want to play better than we did, but even if we don't play brilliantly, we want a result".
"In the 89th minute we make another tactical mistake, we didn't close the gap between Joe (Gomez) and Virg (Virgil van Dijk), and then we can not react anymore".
"We defended with 4-4-2, the same as many other times". That happens. We don't have to think about intensity.
"We have done it better this season, so we can do it - but we have to do it every game".