Under-pressure Fulham manager Slavisa Jokanovic hit out at what he described as an "absurd" situation after Aleksandar Mitrovic appeared to have headed the bottom-of-the-table visitors into the lead five minutes before the break.
Celebrations were cut short by the offside flag, however, and a quick restart from Liverpool goalkeeper Alisson allowed Trent Alexander-Arnold to play in Mohamed Salah for his eighth goal of the season and his 34th in his last 36 games at Anfield.
Just 14 seconds separated the flag and the Liverpool opener and when Xherdan Shaqiri stretched the lead with a delightful volley eight minutes into the second half the game was beyond the visitors.
Klopp was unsure of whether the officials had been right to deny Fulham a goal but hailed the "brilliant" reaction of his Premier League title-chasers in turning the situation to their advantage.
"I saw it once, I'm not sure if it was offside or not," said the Liverpool manager. "We didn't get a goal against Arsenal when we scored a clearer goal. I don't want to compare it but you cannot change it.
"The most important thing is reacting in a situation like that and that was brilliant. Ally, Trent, Mo and done, it was a fantastic situation."
The German boss also felt Andy Robertson had been impeded in the run up to Fulham's disallowed goal and it was the Scottish full-back who could have played Mitrovic onside.
"Good routine. At the end we were a bit lucky," admitted Klopp.
- 'Disrespect' annoys Jokanovic -
For Jokanovic, there was no doubt that his side's possible opening goal should have stood.
"Robertson didn't sufficiently squeeze up and my player is onside and scored a goal. In one moment, a crucial moment, we go from one goal up to one goal down," said Jokanovic.
"In this country you normally can't show some disrespect to referees but it's a problem (when they) show disrespect to my team, myself, and the Fulham supporters.
"The situation can be a little complicated but you must be sure to take this kind of decision."
Jokanovic admitted his team could have reacted better to Liverpool's swift break but said it shouldn't have existed in the first place.
"We didn't defend well this counter-attack but this counter-attack shouldn't exist. It's a completely absurd situation we have to defend."
Liverpool had created several reasonable chances before the opening goal -- Sadio Mane, Salah and the influential Shaqiri all going close -- but Fulham had almost scored first when Ryan Sessegnon capitalised on Joe Gomez's mistake to close in on goal only to drag his shot wide.