For the second successive home match against a newly-promoted team, Kenny Dalglish's side failed to convert their chances.
Carroll's was the miss everyone will remember, although there were enough opportunities created afterwards to have prevented a third draw in a row at Anfield.
The £35million club-record signing side-footed against the crossbar from just six yards with the goal at his mercy.
In the end they were fortunate to escape with a draw as Swansea improved as the game progressed and could have snatched victory in the closing stages.
It was only the second point away from home this season for Brendan Rodgers' side but, on the strength of their performance alone, they were well worth it.
Liverpool have hit the frame of the goal more than any other team this season and they made that unwanted tally 10 in only the seventh minute with a chance which Carroll should have buried.
Charlie Adam's through-ball down the inside-left channel was picked up by Stewart Downing whose low, teasing cross into the six-yard box required only the simplest of touches to convert but the big striker leant back and somehow crashed his shot against the crossbar.
Swansea were confident enough in possession without really opening up the home defence but it was a different story at the other end with Luis Suarez flashing a long-range shot just wide, Downing having an effort deflected behind and Lucas Leiva's header dropping the wrong side of the post.
Only a brilliant one-handed reaction save from Jose Reina, on his 163rd consecutive league appearance, kept out Wayne Routledge's inswinging cross intended for Danny Graham.
But Swansea counterpart Michel Vorm, who kept a clean sheet for Utrecht at Anfield in the Europa League last season, showed he was equally adept as he got down superbly to tip wide Suarez's shot wide after the Uruguay international had reacted first to Adam's blocked shot on the edge of the penalty area.
Joe Allen was next to try his luck for the visitors with a low, right-footed shot but there was just not enough curl on the ball to get it inside the far post while just before the interval Downing's weak far-post header from Jose Enrique's deep cross was easily picked up by Vorm.
It was no surprise to see Dirk Kuyt replace the ineffective Jordan Henderson for the start of the second half as the Reds resumed their pressure on the visitors' goal with Suarez heading Adam's free-kick into the arms of Vorm.
While Liverpool have been their own worst enemies up front they nearly compounded that problem at the other end when Graham almost robbed Reina just a couple of yards off his goalline as the goalkeeper tried to clear a Daniel Agger backpass.
Swansea were starting to ask more questions of the Liverpool defence and in the 64th minute Dyer's diagonal right-to-left run allowed him to collect a through-ball but Reina deflected his shot behind off his body.
Suddenly the Spaniard was the busier of the two goalkeepers and when he only half-saved Dyer's shot he had to react swiftly to blocked what looked like being a certain goal from Graham on the follow-up.
Carroll's hopes of redeeming himself for that first-half miss were ended in the 74th minute when he was replaced by former Cardiff striker Craig Bellamy.
Carroll did not hang around to see how the Wales international would do as he headed straight down the tunnel.
Liverpool cranked up the pressure with Neil Taylor's last-gasp clearance denying Kuyt, Agger heading over and Adam having a free-kick deflected wide.
With six minutes remaining Mark Gower should have snatched victory for the Swans but he could not keep his shot down from Graham's knockdown.
Kuyt thought he had scored the winner in the 88th minute but he was correctly flagged offside from Agger's header by assistant referee Sian Massey.
There was still time for Vorm, emulating Norwich goalkeeper John Ruddy a fortnight ago, to pull off a brilliant save to deny Suarez and an even better one to tip over Johnson's volley.
Liverpool felt they should have had a penalty in added time when Suarez went down in the area but referee Phil Dowd waved away appeals.
It may have been an eighth successive match unbeaten for Dalgish's side but four dropped points at home to two of the promoted teams does not make good reading for Liverpool's top-four prospects.