The Swans fell behind 2-0 and 3-2 before levelling on both occasions before a Jordan Henderson goal 15 minutes from time denied them at least a point from the contest.
Monk saw Wilfried Bony score a double and Jonjo Shelvey also on target but it was not quite enough for the Welsh club who eventually went down to a team sitting fourth on the table, just four points in arrears of league leaders Chelsea.
"You come here against a team who are pushing for the league title and to come their ground and give them such a good game, to be in it right to the end, shows how well we've done," said Monk who believes Brendan Rodgers’ side are capable of winning the premiership.
"Why can't they win it? They're up there and it's not out of their grasp.
"They've got the players to do it. With the strikeforce they have and the attacking players, there will always be goals in them."
Swansea’s loss sees them sitting 12th on the table after mixing their form over the past three matches.
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