The Reds swept aside their Premier League rivals in emphatic free-flowing fashion thanks to goals from Roberto Firmino, Sadio Mané, Mohamed Salah and Daniel Sturridge.
Liverpool's victory lifted them into second in the league, after netting eight goals in just three games, but also represented a marker being laid down at an early point in the campaign.
And the Liverpool manager felt his side's display could not have been better as they ruthlessly tore through Arsène Wenger's side on home soil.
"Reds need to prove we are capable of great performances every three days"
Klopp insisted that Liverpool have "so far this season" learned "different things" from "each performance and from each game" that they have played
"Watford was not as bad as people wanted to see it because it is not easy to win there and we were close to winning, but we defended the last few minutes too deep because we wanted to save the result," Klopp added.
He insisted that Liverpool "did this already better in the Hoffenheim away game" against what he felt was "an outstandingly strong side" and also "built on this again against Crystal Palace."
"Yes we could not score a lot of goals, but the decisive goal also counts," Klopp continued. "We then played an outstanding game against Hoffenheim [in the second-leg] and then today was the next step and we did it again."
The 50-year-old felt that was Liverpool's "biggest challenge" against the Gunners, insisting that they "need to learn that we can do things like this every three or four days" or else they will "have a problem during the season."
He added: "We wanted to show it today, we wanted to prove to ourselves, we wanted to be spot on from the first second, we wanted to show our desire, we wanted to show our greed and we wanted to show our ambitions against a very strong side."
Klopp admitted that even then "you never know if you then can win the game", but insisted they didn't focus on "winning the game" but more on "the performance."
"The performance was perfect and the result is a result of the performance," he said.
Klopp insisted - in the face of questions about Liverpool's absences, with Nathaniel Clyne, Adam Lallana and Philippe Coutinho all sidelined - that the club's approach "has to be independent from players."
He explained that "if you miss too many" players then a team has "no chance" and "nobody can do the same", adding: "We never thought about who we miss even when we know how big the problems are when you don't have these quality players involved."
He insisted he was not "pleased" about the performance because of this as he "expected it" from his squad - declaring that it is a job that they "have to do."
"You will never hear an excuse that we couldn’t deliver because of this or that," Klopp said, noting how "intense" the Premier League is and acknowledging that he "cannot line up the same 11 players for five or six months" and so must "have opportunities to change different positions."
Explaining the thinking behind Liverpool's line-up, Klopp said they "decided for rhythm and confidence" and "really thought a lot about the line-up" as to how and who they could change.
He said: "They all looked so positive after the Hoffenheim game in training that I thought 'Come on, let's try again'. And obviously it worked."
Liverpool boss pleased by Gomez's "very important" performance
On Joe Gomez - making his second successive league appearance after featuring in the win over Crystal Palace last weekend - Klopp hailed his display as "good" and "very important" for the team.
He reflected on "11 outstandingly good individual performances" from the start of the game, insisting that even goalscoring substitute Sturridge "came on and had his input" while James Milner was "very, very important" and Marko Grujić "did the job."
"We need this of course. Joe needed time to come back in this shape," Klopp said, insisting the defender himself "knows it best" because he is "young."
The German noted that 20-year-old Gomez is "not a lot older" than right-back rival Trent Alexander-Arnold, insisting that the local-born defender "could have played again" but saying: "Because we have the option we can give him a rest in this case."
Klopp said that Gomez's display was "nice to watch" and both "really, really strong" and "really mature" - declaring: "I said [to Gomez] after the game 'Welcome to adult football' because that was 100 per-cent adult football; really strong challenges without ugly challenges, just hard and a real physical presence. It was good."
The international break separates Liverpool and their next game away at Manchester City on September 9, though the closure of the transfer window on Thursday promises club football remains high on the agenda.
Klopp, on whether he expects a busy final few days of the window, said: "We will see. That's not something to talk about here. If players come in, I think it makes sense to think about what we do on the other side [with outgoing players]."
He insisted that Liverpool are "obviously involved in this" but insisted he is "not sure" whether anything will happen and that they "have to wait."
Klopp joked: "With no games, I hope you [the journalists] can enjoy the next five or six days with all the rumours around and all that stuff. I'm not looking forward to it, but it's part of the game."