The Swans had to settle for a share of the points as they were frustrated by West Ham in a hard-fought encounter at the Liberty Stadium.
The home side had the best chances of a dominant first half as Andre Ayew headed over and Ki Sung-Yueng saw his shot well saved by Adrian.
Swansea continued to press in the second period, Jack Cork's volley expertly tipped away by Adrian once more while a penalty appeal was turned down after James Collins' hand connected with Ki's effort.
The result means the Swans stay in the bottom three of the Barclays Premier League, with 15 points from 17 matches played.
Swansea City made just one change to the starting line-up as Bafe Gomis - who came off the bench to score in last weekend's defeat at Manchester City - returned in place of Wayne Routledge who missed out with a knee injury.
Jonjo Shelvey returned to selection after sitting out the loss at the Etihad with a thigh problem, with the England midfielder among caretaker-manager Alan Curtis' substitutes.
Franck Tabanou (thigh) and Eder (ankle) again missed out through injury.
The Hammers, meanwhile, travelled to the Liberty without Andy Carroll, Manuel Lanzini, Victor Moses, Dimitri Payet, Diafra Sakho and Winston Reid due to injuries.
Lukasz Fabianski, Angel Rangel (Kyle Naughton, 68), Federico Fernandez, Ashley Williams (capt), Neil Taylor, Leon Britton, Jack Cork (Jonjo Shelvey, 73), Ki Sung-Yueng, Gylfi Sigurdsson, Andre Ayew (Modou Barrow, 83), Bafe Gomis.
Kristoffer Nordfeldt, Jordi Amat, Jefferson Montero, Marvin Emnes.
Adrian, Aaron Cresswell, Alex Song (Pedro Obiang, 72), James Tomkins, Cheikhou Kouyate, Mauro Zarate (Enner Valencia, 60), Mark Noble (capt), James Collins, Angelo Ogbonna, Nikica Jelavic, Michail Antonio (Carl Jenkinson, 84).
Darren Randolph, Stephen Hendrie, Reece Oxford, Joshua Cullen.
The Swans - searching for a first home win since August - dominated the early stages as Bafe Gomis shot wide after five minutes and Andre Ayew headed narrowly over after a fine cross from Neil Taylor.
The best chance, however, fell to Ki Sung-Yueng inside the box but his low strike was well saved by the legs of Hammers goalkeeper Adrian.
At the other end, Mauro Zarate saw a powerful effort well held by Lukasz Fabianski and Mark Noble squandered a good chance after the visitors capitalised on a mistake at the back in a lively opening half an hour.
West Ham slowly grew into the game as the half progressed and Zarate came close once more on 32 minutes as he stung the palms of Fabianski from the right edge of the box.
But Swansea continued to press the visitors at every opportunity and they came close once more before the break as Ayew's effort was tipped around the post by Adrian.
Half-time: Swans 0-0 West Ham
Neither side made any changes at the break, but it was Swansea who came mightily close to breaking the deadlock on the hour mark as Jack Cork's stinging volley was superbly parried away by Adrian.
West Ham then made a change as Enner Valencia replaced Mauro Zarate with half an hour to play at the Liberty.
The visitors then survived a huge penalty shout for the home side as Ki Sung-Yueng's shot appeared to strike the hand of James Collins, but referee Lee Mason waved away the protests.
Kyle Naughton and Jonjo Shelvey were then introduced for the Swans in place of Angel Rangel and Jack Cork, while the Hammers made their second change of the afternoon as Pedro Obiang replaced Alex Song.
But it was another substitute - Enner Valencia - who then came close for West Ham as he cut in from the left before seeing a fierce drive tipped over by Lukasz Fabianski.
Both teams made their final changes with six minutes to play as Modou Barrow replaced Andre Ayew for Swansea, while Carl Jenkinson was introduced in place of Michail Antonio.
And the Hammers came close with five minutes to play as James Collins headed over from a corner from the right.
But it was honours even at the Liberty Stadium as both sides have to settle for a point in SA1.