Brendan Rodgers secured a point from a goalless draw on his return to the Liberty Stadium but will feel his Liverpool side deserved more at the home of former employers Swansea.
The Reds had Jose Enrique's first-half strike ruled out for a marginal offside decision, while teenage prodigy Raheem Sterling rattled the bar and Jonjo Shelvey's late strike was beaten out by Gerhard Tremmel.
Man of the match Pablo Hernandez had Swansea's best chances. The Spain winger curled narrowly wide in the first half before having his low-free-kick brilliantly tipped wide by Jose Reina. Ashley Williams also saw former Swan Joe Allen clear his header off the line.
Despite seeing his side only secure a point, which extended their unbeaten league run to eight games but keeps them below Swansea in the table, Rodgers will have taken heart from another promising performance as he looks to rebuild at Anfield, with Sterling, Enrique and Glen Johnson excelling.
Johnson should have given Liverpool the lead from Steven Gerrard's corner after Allen had dispossessed Leon Britton. Wayne Routledge forced a sharp near post save from Reina after turning on the edge of the area, but the game was being played almost exclusively in the Swansea half.
Luis Suarez should have capitalised when Swansea again surrendered the ball, but strayed offside, before Enrique steered narrowly wide from Sterling's superb cross. Swansea were limited to counter-attacks, and one sharp break saw Hernandez go wide of the far post.
Angel Rangel's brave block denied Suarez a simple finish, before Sterling struck the bar with a thunderous volley. Enrique had the ball in the net after 34 minutes from Suarez's delicate pass, but the assistant referee ruled offside, although replays suggested he may have been level.
Michael Laudrup brought Ki Sung-yueng on for the anonymous Itay Shechter at half-time. But the visitors still looked the more likely to break the deadlock, with Tremmel beating away a fierce angled drive from Suarez.
The hosts then enjoyed their best spell of the game. Michu had a header saved by Reina before Allen denied his former team by clearing a Williams header off the line at the far post.
Suarez and Sterling broke from a Swansea corner but a laboured pass from the winger forced the Uruguayan wide and Tremmel held his shot. Hernandez forced Reina to make a superb fingertip save late on, before Tremmel blocked Jonjo Shelvey's fizzing strike to ensure the points were shared.