The Welsh club needed a 10-goal turnaround to send Southampton down instead, which, unsurprisingly, was never a serious possibility.
They did take the lead through midfielder Andy King, leading to optimistic chants of "we want 10" from home supporters.
But by halftime Swansea, without an away win in 13 previous away games, led with goals by Senegal's Badou Ndiaye and then Peter Crouch. Xherdan Shaqiri even missed a penalty for Stoke.
Swansea's Portuguese manager Carlos Carvalhal is widely expected to leave, five months after arriving.
"I talked with the owners yesterday, we will talk again on Monday," he said.
"I will think about Swansea and myself. I must talk with my family. After that I will make the right decision about my future.
"I know the Championship and reached the play-offs twice. It's not common for a team to reach the play-offs two years in a row."
Later on Saturday the club's majority owners, Americans Stephan Kaplan and Jason Levien, issued a statement agreeing there had been "mistakes along the way" without offering any clarification about the manager's position.
"Nobody at Swansea City is making excuses, least of all ourselves," they said. "As owners, our commitment is total and the determination to regain Premier League status is our only focus.
"Perhaps the club has lost its unique identity, the special essence that made Swansea City different -- better, in many ways -- and we need to rediscover that identity both on the pitch and off it if we are to make the community proud of this football club again."
Stoke manager Paul Lambert, like Carvalhal, also said his time in charge was not enough to turn things round after being appointed in January.
"There were things wrong, without a doubt," he told the BBC.
"We drew games that we should have won. A little bit more quality across the top (positions) and we wouldn't be in this position.
"There's a core of players, but there's a turnaround that needs to happen."
(Reporting by Steve Tongue, editing by Pritha Sarkar and Ian Chadband)
