There were four changes in the Seasiders line-up despite their 3-0 midweek victory over Sheffield United.
Swansea almost took the lead after two minutes when Darren Pratley raced into the area unmarked but his attempted lob was clutched by Blackpool keeper Matt Gilks.
The visitors played some neat football in midfield but too often they delayed the final pass and their strikers were caught offside.
The Swans looked far more dangerous when they were attacking and Craig Beattie fired low from a Mark Gower corner midway through the half only for Gilks to gather the ball on his knees.
In the 28th minute, Butler had a free header from Gower's cross but was well wide with his effort.
The Swans should have had a penalty in the 38th minute when Beattie was bundled over by Charlie Adam but referee Andy Hall waved play on.
Two minutes into the second half, a Gower corner went straight across the Blackpool goalmouth with Butler just failing to get the final touch.
The Swans were well on top and a 54th-minute shot from Gower was pushed away by Gilks as Blackpool were pinned back in defence.
Three minutes later, Gilks dived to push away a Butler free-kick and then Beattie blasted just over with the keeper beaten.
Beattie was involved in the action at the other end when David Vaughan's centre looked to be heading for the corner of the Swansea net but the striker made a superb last-ditch tackle and cleared the ball from under the crossbar.
Lee Trundle came on for Beattie in the 77th minute closely followed by Gorka Pintado as the Swans went looking for victory.
Substitute Nathan Dyer had a fleeting chance in the closing minutes but the Swans were unable to get the goal they deserved.