The Reds travelled down to the South Coast without Joel Matip, Philippe Coutinho and Daniel Sturridge but appeared unhindered, going 2-0 up inside 22 minutes courtesy of Sadio Mane and Divock Origi's efforts.
Within just a few minutes of the second-half, Callum Wilson halved the deficit from 12-yards after James Milner had conceded a penalty on substitute Ryan Fraser.
Emre Can's wonderful curling strike into the top corner up the other end shortly after looked like it had put the game out of reach, until Fraser - and then Steve Cook - scored in the game's closing stages to bring Bournemouth back from the brink.
Having trailed 3-1 with 15 minutes to go, defender Nathan Ake completed a stirring comeback late on - bundling in after Loris Karius had spilled Cook's shot from distance in stoppage time.
That condemned Liverpool to their first defeat in all competitions since losing out to Burnley back in August and just their second of the season.
But despite acknowledging the disappointment of losing after being in commanding control of the game at half-time, Klopp insisted he was not angry with his side.
Klopp: Wonderful story unless you're on the wrong end of it
"In all our good moments, it was pretty clear who were the better side," Klopp remarked in his post-match press conference, insisting that Bournemouth "wanted to press high and early" but "had no chance for it."
He praised his side's "really good football" and how they were "quicker in all our decisions", insisting that they "wanted to mix up our passes a little bit" due to Bournemouth's pressing tactics.
The German said that they fielded Origi and Mane up front to "use in these situations" which they "did twice very well" to go 2-0 up.
Yet he was disappointed that they "didn't play too well" after establishing a two-goal lead, adding: "I told the boys at half-time that the first-half was perfect preparation for the second-half because we already showed that at 2-0, the game is not done."
Klopp insisted his team were "too static" with their passing and "kept the ball too long in the wrong moments", as well as "passing too late" so that the recipient of possession was immediately "under pressure."
He declared that "everything changed" because Liverpool "lost a little bit of concentration", insisting the penalty "changed the game a little bit" and that it "happened quite quickly again" after his team scored "the third one, a wonderful goal."
"We opened the door, but Bournemouth had to run through it and they did that," explained Klopp, who insisted that he "of course" is "not happy with the result."
He admitted his opposite - Cherries boss Eddie Howe - was "on fire" and "pushed the boys up" even after his side equalised to make it 3-3 late on, calling it "a wonderful story if you're not on the wrong side."
He said that they "have to accept" that they "were on the wrong side" on this occasion but said insisted Liverpool "have to learn from it" and "will do, for sure", reassuring that "everything will be good again."
"Reds had 'big impact' on both sides of the game"
Asked whether he was infuriated by his side's late collapse - which ended a 15-game unbeaten run in all competitions - Klopp said that he was "angry a few times" during the game when he "still had influence" on the result but claimed that he was not after it ended.
On the manner of the game, and Bournemouth's late surge of momentum, Klopp insisted that it was "not too simple to come back" and that is "why you have to keep the momentum all the time or as long as you can."
"But now it has happened, I cannot change it anymore so why should I be angry?" questiond Klopp, who said his side "didn't want to lose" and "worked hard enough" but simply "were not clear enough in the right moments" and "had no influence" on "a few things in the game."
He felt that the penalty was "very important" and said that "on the other hand" there was a situation with "a clear foul" on one of Roberto Firmino or Origi which should have warranted a "second yellow card."
Klopp bemoaned that there "could have been a few situations differently" which would have meant they are "on the better side with the same game" but said they "need to accept that there's no coincidence that it happened" and that they "had a big impact on the result on the good side and on the bad side."
The Reds boss also remained insistent that the loss in no means reflects a lack of backbone or a weak mentality within his squad, and that their reaction to the result will say more about them and their quality.
"We have no attitude problem. We have no character problem," Klopp continued to tell reporters, insisting that "nobody is born as a winner" and instead "you need to learn it."
He noted that there "was a lot of criticism" for their performances and results last term after finishing ninth and said that now they "try to be much better", adding: "I would say if you know about the problems, it's easier to handle them. I knew that it [this result] could happen. Now it has happened and now we have to deal with it."
Klopp: Criticism does not affect my belief in this team
Klopp was also stern in his defence of first-choice goalkeeper Loris Karius, who came in for flak after a below-par performance.
The German, signed from Mainz to fight for the gloves with the club's other shot-stopper Simon Mignolet, was particularly culpable for substitute Ryan Fraser's strike and Ake's late winner.
He said that criticism is "absolutely no problem" and vowed: "If you have quality, you will get stronger from it. I respect and accept everything you [the media] will say about us. If you want to say we are blind, silly, not good enough, whatever, do it. It has no influence on what I think about my team."
Klopp once again acknowledged that his team "made mistakes" but declared not finishing their chances does not necessarily mean that they don't have "good strikers."
He reflected that Ake's goal "was not the most lucky situation for a goalkeeper" and added: "If Loris had made a real decent save, I would have wished for it, but it says nothing about him as a goalkeeper. It only happened, and now we go on."