Swansea's gap to the relegation zone was cut to one point after Southampton's 2-1 home victory over Bournemouth - and it is now six games without a without a win for Carlos Carvalhal's side.
Cesc Fabregas' fourth-minute strike - his 50th in the Premier League - condemned Swansea to a one nil home defeat to Chelsea -their first home league defeat since January 2nd.
And Swansea must hope top scorer Jordan Ayew avoids retrospective action for a late challenge on Gary Cahill when the striker appeared to catch the Chelsea defender in the neck.
Asked about Ayew's challenge, Carvalhal said: "I don't want to (distract) too much from what we did with referee situations. I don't want to disturb my focus.
"The negative is we lose, the positive is we played against a strong team like a strong team plays.
"When we arrived we were five points to the teams above, we depended on others to try and get out of this position.> "In this moment we just depend on us, it's something we have in our hands.> "We must look to the games that we have - Bournemouth, Southampton and Stoke - to try and achieve the necessary points to stay in the division."