Fulham manager Slavisa Jokanovic said referee Paul Tierney showed "disrespect" to his team after disallowing a header from Aleksandar Mitrovic, which allowed Mohamed Salah to score 14 seconds later for Liverpool.
Replays showed the decision for Mitrovic's effort was a borderline call, with Liverpool left-back Andrew Robertson appearing to be in line with the Serbia forward.
The decision angered Jokanovic, whose team remain bottom of the Premier League after their sixth successive defeat.
"When I check the clips now it's Robertson (who) hasn't done a good enough job to squeeze up and my player is onside and scored the goal," he said.
"In one moment, a crucial moment, instead of 1-0 up we're 1-0 down.
"We can talk about this situation for hours, but the damage is done. It's a completely absurd situation to defend.
"In this country normally you cannot show disrespect to the referee and this is a problem because it's shown disrespect to my team, myself and Fulham supporters."
Salah's goal came after goalkeeper Alisson initiated a lightening counter attack, with the Egyptian running unopposed from the halfway line to open the scoring.
"We were a bit lucky and maybe because of Robbo it is not 100% offside because of his heel," said Liverpool manager Jurgen Klopp.
Xherdan Shaqiri's cushioned finish in the second half confirmed victory for the Reds who equalled their best start to a Premier League season, which came in 2002-03.
Klopp has maintained his Liverpool team are not yet at their free-flowing best - and that in itself should swell confidence around Anfield.
This victory ensured the Reds remain unbeaten after 12 league outings, eight points better off than at the same time last term and well placed to challenge for the league title.
Last season Liverpool toiled against the bottom three, drawing twice against West Brom, once against Stoke and losing at Swansea.
But Salah, who has now scored five goals and provided five assists in 633 minutes against newly promoted teams, helped to ensure the outcome of this fixture was not in question.
The Egyptian had scored nine times at the same stage last term but his performance against Fulham, where he registered his sixth goal of the campaign, suggested he is not far from replicating his best form.
The 26-year-old instigated a glorious early exchange with Roberto Firmino to carve the visitors' defence apart, only to see Rico react well to save at his feet.
And that was a precursor to what was to follow, with Rico again saving from the Egyptian before he broke clear to open the scoring.
"The most important thing is reacting quick in that situation and it was brilliant: Alisson, Trent (Alexander-Arnold), Mo and done," Klopp added.
Aleksandar Mitrovic thought he had given Fulham the lead at Anfield, but Mohamed Salah scored 14 seconds later for Liverpool after the Serbia forward's header was ruled out
Fulham, whose expansive style of play proved so successful in the Championship last season, have yet to deliver results against clubs in the Premier League.
The Cottagers, who spent more than £100m on players in the summer, arrived at Anfield with the worst defensive record in the league, having conceded 29 goals from their opening 11 fixtures.
That prompted Jokanovic into a rethink as he deployed four central defenders in a revised system and fended off pre-match questions about his team selection.
And after early teething problems - with Sadio Mane firing wide from Trent Alexander-Arnold's cross - Fulham grew into the game.
Happy to concede possession and sit deep, the visitors could have delivered the perfect riposte of a goal when Ryan Sessegnon was sent clear by Mitrovic's flick-on.
The England under-21 winger, who covered more ground (12.22km) than any other player during the course of the afternoon, guided his shot wide of the right-hand post.
German forward Andre Schurrle then tested Alisson and Mitrovic failed to connect properly with a shot from 10 yards out.
When the Serbia forward powered a header past Alisson from Tom Cairney's cross it appeared as though Jokanovic's strategy might yield an unlikely dividend.
Instead the visitors, who managed the same number of shots on target as Liverpool in the first half, were undone by a moment of naivety with Denis Odoi's attempt to catch Salah offside.
Mohamed Salah has now scored against 19 of the 21 Premier League opponents he's faced with Liverpool, failing only against Man Utd and Swansea
Liverpool travel to Watford for their next Premier League fixture on Saturday, 24 November (15:00 GMT) while Fulham host Southampton on the same day (15:00).