However, the Blues have qualified for the knockout stages of the competition after Schalke 04 could only pick up a point away against Steaua Bucuresti.
Here, Sports Mole takes a closer look at the action between the two sides in Switzerland.
On target 7
On target 0
Was the result fair?
Most definitely. Basel came out of the blocks at such a pace that Chelsea never got an opportunity to settle into the game. Chelsea were reliant on Petr Cech keeping the game level for the majority of the first half, but there was little that he could do to prevent Mohamed Salah netting the winning goal.
Given that Basel have deservedly beaten Chelsea on both occasions over the past couple of months, it makes you wonder how they have only picked up two points from their other three games. The Swiss outfit play with fluidity and pace, and Chelsea have struggled to create anything against them in either match. They deserve to qualify for the next stage, but first they must avoid defeat to Schalke.
This was as inept as it should get for Chelsea. Mourinho would have been fuming about their failure to halt Basel's momentum during the opening 30 minutes, but he will undoubtedly be more worried with their performance in attack after failing to register a shot on target. Striker Samuel Eto'o also looks to have picked up a serious groin injury that could keep him out of action until after Christmas.
Sports Mole's man of the match
Petr Cech: Basel were collectively superior to Chelsea in all areas of the pitch, but there wasn't a standout performer for the hosts. On that basis, I am going to hand the award to Petr Cech, who played a vital part in keeping Chelsea in the game for as long as he did. No save was particularly outstanding, but he did what he needed to when called upon.
It wasn't so much of a gaffe, but Branislav Ivanovic got caught out of position for Basel's goal, and Jose Mourinho indicated as much with his gestures from the touchline. The Serbian defender had performed solidly up until then, but he is likely to be on the end of some stern words from his manager.
Stephane Lannoy put in a competent display in Switzerland, and he had a case for handing out four cautions. The Frenchman did award 38 free kicks throughout the match, but it wasn't noticeable. The 44-year-old can be content with his performance tonight.
Basel: Basel have two weeks to wait until they return to European action to try to progress through to the knockout stages. It's likely to be a tight game in Schalke, but on this outing, they are capable of causing what would be considered a minor surprise.
Chelsea: The Blues have three Premier League fixtures in their way before they can focus on their final game with Steaua Bucuresti. Despite their qualification, Mourinho will be well aware of the importance of earning three points to confirm their position at the top of Group E.