The Reds led 4-0 by half-time thanks to a Mohamed Salah brace and efforts from Roberto Firmino and Philippe Coutinho, before second-half goals from Firmino, Alex Oxlade-Chamberlain and Trent Alexander-Arnold sealed the club's biggest ever European away win.
Despite the finding the goalscoring form that Liverpool have craved for some time at the Ljudski Vrt Stadium, it was the manner in which his charges carried out their tactical instructions that most pleased Klopp.
"A few of our goals came directly from our counter-pressing"
On Liverpool's performance, he told his post-match press conference: "Good. Or even better. From the first second it was exactly what we wanted to do."
He declared that the visitors "wanted to show the best counter-pressing of the last few weeks" as Klopp insisted the way they protected their "offensive movements, patterns and all that stuff" was "already really good against [Manchester] United."
"But we could have done even better in counter-pressing," he explained. Tonight we did much better and against a football-playing side like Maribor, it made a lot of sense."
The German highlighted Liverpool's first goal as coming "from a pressing situation" and hailed that "a few other goals were after a counter-pressing situation" and so their game-plan "helped a lot."
His side having developed a recent tendency to waste good goalscoring opportunities, Klopp was pleased that how Liverpool "finished these situations was also good."
He bemoaned: "A lot [of times] this season already [we have been] alone in the box to make a cross or a pass, but were not relaxed enough to play the right pass. Tonight it was different."
Klopp felt that when Maribor had the opportunity to play they "played immediately" and were "around our 18-yard box" which "showed how good they could be."
But he added that Liverpool "never gave up in this game" particularly in the second-half and praised the "all-round" performance of his team which he felt was "really, really good" and was "really happy" with.
Reds did "unbelievably well" but must build on it - Klopp
Liverpool's win in Slovenia is both a new club record away win but also the most emphatic victory for a British team away from home in Europe's premier competition.
Reacting to the news of his side's new record, Klopp said: "I was told immediately after the game, I had no idea actually. We spoke a few times about how the wonderful history of this club can sometimes feel like a backpack so it's nice to write history, and it will probably be difficult to beat that. It's quite rare that you win 7-0 but it shows again we did unbelievably well tonight."
Klopp felt that Maribor were "quite confident before the game" because they "are a very good team", noting that the local newspapers in the morning were bullish that "an English team had never won in Maribor."
"That's obviously another thing that we did for the first time," Klopp beamed, insisting that his Liverpool players "deserved that because they really kept on going."
He declared it "just good to work together" with the squad at his disposal but lamented: "The only problem is that you always have to explain why you didn’t win."
The Reds boss said of their recent problems that they are "probably not the most difficult thing to explain" because "you see we created the chances but we did not use them."
Klopp told the press that such reasoning is "not enough" for them and that they have to "put the finger on all the problems we sometimes had" which made it "a challenge."
He said that it will "be a challenge to stay confident in this league" but vowed to "try to use the result [against Maribor] now."
However, Klopp warned that their next game is against title hopefuls Tottenham Hotspur and so "it's pretty likely it will not be a similar result."
"We have four or five days to recover and prepare for the game, so that's good and we are already looking forward to it," he said.
Goal will "help" Oxlade-Chamberlain
Among the many positives, deadline day signing Oxlade-Chamberlain opened his Liverpool account with a cool-headed finish late on, dispatching Daniel Sturridge's clever through ball.
Klopp believes his first goal "helps a lot" but joked that the midfielder "could have scored two."
On the goal itself, Klopp said: "It was nice from Daniel, how he made this goal. It was really cool and I liked it."
The manager said of Oxlade-Chamberlain's general display that he was "very active" and while "was involved not immediately" because his teammates "didn't involve him", they began to recognise that he was there and "he was really involved and it was good."