It was the 39-year-old manager's first return to his former club and despite a lively first half, both sides struggled to find any fluency going forward after the break.
In a game of few clear-cut opportunities, Liverpool went closest to breaking the deadlock in the first half, but Jose Enrique, continuing in a more advanced role on the left wing, saw a goal disallowed for offside after a deft cross into the back post from Luis Suarez.
Swansea manager Michael Laudrup made two changes to the side that beat Newcastle 2-1 last weekend, with Chico and Wayne Routledge coming into the team for Garry Monk and Nathan Dyer, with striker Danny Graham missing out altogether after failing to recover from illness.
Liverpool boss Brendan Rodgers handed rare league starts to both Stewart Downing and Jordan Henderson, with Suso dropping to the bench and Andre Wisdom missing out with a knee injury from the 3-0 win at Anfield over Wigan last time out in the league.
With the game played at a lively tempo, the home side carved open the first decent chance of the game in the 11th minute when Routledge forced Pepe Reina into a smart stop down low at his near post after a flowing move.
This prompted a response from Liverpool, though and the club should have taken the lead shortly afterwards when a superb low cross in from the right by Glen Johnson saw Jose Enrique get in front of his marker only to chest the ball narrowly wide when just six yards out from goal.
It took a magnificent save from Tremmel to deny Johnson when he was played through one-on-one by a tidy reverse pass by Jose Enrique in behind the back four, with the fullback's finish deflected over the bar.
Hernandez nearly found the inside of the far right post with a curling effort on the half hour mark from the edge of the box after displaying some quick feet to take it round Allen, with Reina looking well beaten before the ball flashed past the post, before Suarez saw a shot well-blocked by Rangel.
From the resulting corner, Sterling took down the clearance before unleashing a fierce drive which came straight back off the crossbar with Tremmel rooted to the spot. With Liverpool well on top, the club had a goal chalked off for offside in the 33rd minute with Jose Enrique's tap-in at the far post from Suarez's delicate cross correctly ruled out and they went in at the break with the scores level.
Liverpool started the stronger of the two teams in the second half and Suarez brought out a good stop from Tremmel with a powerful strike from a narrow angle after a sustained spell of possession from the visiting side, but Swansea responded by going close with a Michu header on the hour mark.
With the half slowly but surely coming to life, Ashley Williams saw his header cleared off the line after a corner by Allen before Suarez and Sterling combined on the break after a Swansea corner only for the Uruguayan to see his effort fly straight into the goalkeeper's arms in the 82nd minute.
Reina had to be at his best to keep a Hernandez free kick late on down low to his left, before substitute Jonjo Shelvey went close with a stinging strike from the edge of the box which was clawed away by Tremmel. With little to separate the two sides, a draw seemed a fair enough result on the balance of play.
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