Richarlison netted a second for the visitors seconds from half-time before Gini Wijnaldum sealed the game with a goal in the closing stages of the 90 minutes.
The result sees Liverpool set a club record of 32 games unbeaten in the league and the boss was delighted with the manner in which they managed victory.
"Good – really, really good, especially in the circumstances I created pretty much by myself with the line-up," Klopp said of the win. "Making five changes can lead to some problems, of course. I didn't see any of them.
"We have to make changes, that's clear; probably some people were not too happy that we did that before a derby but we cannot make differences on that. It was clear it would be a really intense game so we needed fresh legs, as many as we could get.
"The only two boys I didn't bring tonight were Joe [Gomez] and Naby [Keita] and both – with Joe you saw it and Naby I can tell you – are in outstanding shape. It was only me not being brave enough to make [those changes] as well.
"But what the boys made of this difficult game was exceptional. We scored incredible goals. We had to fight. A few things didn't work out defensively.
"First, we probably surprised them with our system; then, they didn't surprise us but we couldn't adapt as quickly as possible as necessary to their little system change.
"We wanted to wait until half-time – I was fine with 4-1, I was not fine with 4-2. But then we adapted to the system.
"It was an intense game but we controlled it much more again, scored a sensational fifth goal and job done – all good."
Klopp also praised goalscorer Shaqiri, who was making his first start in seven months, whilst he hailed Origi's performance and two goals.
"Outstanding! What a game he played. It was not only the goals but the goals were exceptional," Klopp said of the Belgian.
"The first one was a great attack in general – winning the ball, Adam [Lallana] passes to Sadio; Sadio sees the run, sees his movement and passes that ball in exactly the right moment, one touch and an open goal, great.
"The second one... in Germany when I was young one highlight of my week was always goal of the week and goal of the month; when they selected these, that would have been 100 per cent in contention.
"It was just a great first touch and then finishing it off like this. Apart from that, incredibly important runs for us, movements, used his speed, looked so natural. That was the most important thing.
"The understanding with Shaq and Sadio was obviously really good. So it was a pretty impressive performance of Div."
Liverpool are back in action on Saturday as the games come thick and fast during a hectic December schedule.