The reds dominated possession throughout the game, but the opening 20 minutes saw few touches for the temporary striking partnership of Daniel Sturridge and Divock Origi. Okay, no foul but Joe Gomez is injured'. Xherdan Shaqiri netted in injury time to make the game secure.
Burnley manager Sean Dyche made no apologies for his side's approach as the hosts picked up just one yellow card, but Klopp added: "I'm pretty sure saying this won't make me a lot of friends here, but that's not the job I have". Even Burnley's teamsheet revealed five changes of their own. Andrew Robertson, Sadio Mane and Dejan Lovren did not travel.
Salah and Firmino did then come on then, and the latter had a goal inside four minutes from what looked like a training-ground move.
The contrasting fortunes of Liverpool FC and Burnley FC likely will be clear for all to see.
Although the reds were not significantly troubled, the reds took time to adjust to the pace of the game. Trent Alexander-Arnold came on to replace the youngster in the first-half.
"Burnley had a specific plan to be really aggressive and really physical", said Liverpool's German boss.
Burnley continued to ask questions of the Liverpool defence and found an opener soon after the restart when Jack Cork poked home from very close range after Allison had turned away to rapid-fire efforts from James Tarkowski and Ashley Barnes.
The reds response was fairly swift.
However it was Naby Keita in the middle of the park who was good throughout, and was unlucky to be denied a goal through a fine save from Joe Hart.
Virgil van Dijk - who was the recipient of a freaky assist against Everton - then provided another as he squared for Firmino from Alexander-Arnold's ball in to the box. You get the ball, nice, but then, boom, you get the player as well.
Arms folded he stood in front of the Liverpool fans. But their class showed with Milner's terrific finish and a well-worked free-kick narrowing the gap to City back to just two points.