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."