The Swans suffered a narrow 1-0 defeat at Liverpool following a contentious 62nd-minute penalty from James Milner.
Milner converted from the spot after Jordon Ibe's cross struck the arm of Neil Taylor inside the box shortly after the hour-mark.
But in testing conditions at Anfield, the Swans limited their in-form opponents to few opportunities while Lukasz Fabianski remained largely untested throughout the 90 minutes.
The Swans rallied late on and pushed for an equaliser, but despite cranking up the pressure on the Liverpool back line, they were unable to snatch the elusive leveller.
The Swans make just one change from the side that drew 2-2 with Bournemouth last weekend as Gylfi Sigurdsson returns to the starting line-up in place of the suspended Jonjo Shelvey.
Liverpool, meanwhile, make two changes from the side that beat Manchester City 4-1 last time out as Jordon Ibe and Christian Benteke come in for the injured Philippe Coutinho and the suspended Lucas Leiva.
LIVERPOOL: Simon Mignolet, Nathaniel Clyne, Martin Skrtel, Dejan Lovren, Alberto Moreno, Emre Can, James Milner (capt), Jordon Ibe (Kolo Toure), Roberto Firmino (Jordan Henderson, 65), Adam Lallana, Christian Benteke (Daniel Sturridge, 71).
SUBS: Adam Bogdan, Joe Allen, Divock Origi, Connor Randall.
SWANS: Lukasz Fabianski, Kyle Naughton, Kyle Bartley, Ashley Williams (capt), Neil Taylor, Leon Britton (Jack Cork, 65), Ki Sung-Yueng, Andre Ayew, Gylfi Sigurdsson, Wayne Routledge (Jefferson Montero, 72), Eder (Bafe Gomis, 69).
SUBS: Kristoffer Nordfeldt, Angel Rangel, Federico Fernandez, Matt Grimes.
Chances were few and far between during a blustery first half at Anfield.
Despite the hosts coming close to opening the scoring early on, when Kyle Bartley diverted the ball onto his own post following a sliding challenge on Reds winger Jordon Ibe, the home side were unable to truly test a resolute-looking Swansea defence.
For all of Liverpool’s possession, they struggled to fashion a clear-cut opportunity as the Swans displayed their resilience and grew in confidence as the half wore on.
Following the host’s early opportunity, Eder came closest to breaking the deadlock for the Swans when he headed wide of the target after rising high to meet Kyle Naughton’s inviting cross.
With just under five minutes left of play in the first half, Liverpool left-back Alberto Moreno then saw his 20-yard free-kick swerve over the bar.
HALF-TIME: Liverpool 0 Swans 0
The two sides remained unchanged at the start of the second period.
The first sight on goal fell to the Swans as the ball dropped to Ki Sung-Yueng, 25 yards from goal, but the South Korea international fired his effort over the bar.
As was the tale of the first half, Liverpool continued to enjoy the lion's share of possession without truly testing Swansea's goal.
Lukasz Fabianski was forced into making his first save of the afternoon, seven minutes into the restart, when he turned Ibe's driven effort from distance around the post, while Dejan Lovren saw a looping header fly harmlessly over the bar.
But the deadlock was broken on the hour-mark when James Milner converted from the penalty spot after Neil Taylor was adjudged to have handled the ball inside the box.
In an attempt to find a way back into the game, Swans boss Monk introduced Jack Cork, Bafe Gomis and Jefferson Montero into the fray, replacing Leon Britton, Eder and Wayne Routledge.
With 15 minutes left on the clock, Milner nearly doubled Liverpool's lead but dragged his shot wide of the far post following good play by substitute Jordan Henderson.
But as the game entered its final ten minutes, the Swans began to crank up the pressure on Liverpool's goal as the home side looked to hold out for victory.
Montero nearly capitalised on a defensive error from the hosts, only to see his shot at goal blocked by Martin Skrtel, while Gomis saw an effort from 30 yards deflected wide.
The Swans continued to cause a sense of panic with the home side's back line with a series of corners late, but they were unable to find the elusive equaliser.