Philippe Coutinho's curled effort from long range set the tone after just six minutes although Klopp's men were wasteful throughout the rest of the first half and failed to immediately kill the Swans off.
But a second-half barrage saw Liverpool score three more goals by the 66th minute, Roberto Firmino's brace either side of Trent Alexander-Arnold's first Premier League goal for the club making it 4-0.
And Alex Oxlade-Chamberlain's first strike at Anfield, a lovely lifted volley into the far corner, completed a comfortable rout in Liverpool's penultimate match of 2017 - a result that lifts them back above Tottenham Hotspur into fourth place.
Klopp disappointed with Reds' pressing after having to work "hard" to beat Swans
Analysing the match afterwards, Klopp told journalists that "you can say a lot" about their pre-match team work and their plans on beating Swansea, but called it "always different" to see such blueprints realised "in the game."
He noted that the South Wales outfit are "a different team to play against" because they "play real football" and insisted the Reds' "main tool or weapon should have been counter-pressing."
"Because you cannot come through with all the balls but very often if you lose the ball and then the next second it's 80 yards away, but Swansea are playing football," he reflected.
But Klopp felt Liverpool's timing "was not good in the situations" and that also their "formation was not good in these situations" and so they "were always a bit too late" to the ball and Swansea "could play" around them as a result.
Yet the German acknowledged that the visitors "didn't get a lot of chances" bar "one or two half-chances", declaring that regardless the match was "quite intense" and that "the way was always really long to come back into the right positions [in] the right situations."
He added: "Even in a not perfect, not really good first half, we had enough chances to score two or three goals so that should be enough."
Klopp dismissed suggestions that he was disappointed his side led only by a single goal at the break, but insisted he told them they needed "to defend the situations much better" and "had to be more compact."
"In a few moments we were kind of man-orientated, that's only allowed in our own box, so we had those few problems and we did better in the second half," he declared.
Klopp noted that Liverpool "scored the first three goals after counter-pressing situations" but admitted: "It looks like after the game, it's 5-0 and you think 'wow, easy game!' but it was not. It was really hard work."
He said that he has "no problem" with his side having to produce industrious displays to win such games and insisted he is "really happy" about the things they have "learned from the game."
"It's a perfect result for us, nobody got injured as far as I know, very important three points, five goals, clean sheet, all good," he beamed.
Klopp: Liverpool forwards will score goals no matter who plays
This was the fourth time this season that Liverpool have scored five goals or more in a single match, with league leaders Manchester City the only team to equal such fine form in front of goal.
Indeed, Premier League champions elect City (77) and Paris Saint-Germain (89) are the only two clubs from Europe's five major leagues in England, Germany, Spain, Italy and France to score more than Liverpool's tally of 75 across all competitions this term.
Coutinho extended his total to 12 goals and eight assists while Firmino's second-half double - following on from a goal and an assist in both of his last two outings - means he now has 16 goals in the league and Champions League this season.
On the Brazilian forward's form, Klopp insisted that he is "happy for all of the boys when they score" but said: "I couldn't say how many he has. I don't care to be honest. It's not in my interest."
Rather, the Reds boss focused on Liverpool's team play and insisted that if they play as they did "in the good moments" against Swansea then "the boys will be in different situations and it'll be easy to score."
He specifically referenced Firmino's second for proof, joking to gathered media that anyone of them - or even himself - might have been able to tap it in such was the clear-cut chance they created.
"That's what you have to do, you have to work for that and everybody could see Mo [Salah] was not the happiest person in the stadium when we took him off," Klopp said, hinting at their front-line's desire to score more goals.
Yet Klopp warned that he must "stay kind of reasonable or serious" and continue to rest his star players because "there's a lot of games to come" and whichever of Salah, Firmino, Coutinho and unused substitute Sadio Mané play, "they will all score goals."
He explained: "Sadio did not play tonight, but he will score if we play like this, if we bring the different players, in the different moments in the situation."
Returning to the topic of Firmino's form, the manager insisted that he "appreciates always his effort and his performance", calling himself "happy" that he scored twice.
He even suggested that he cannot specify "how many goals" Firmino has scored so far this season because "he is always involved" and "always in and around the really dangerous situations for the opponent."
He continued: "First half he helped left full-back to right full-back, he was everywhere. In the end he scored two goals, so that's nice."