The Portuguese endured a nightmare return to Stamford Bridge, not only suffering a humiliating 4-0 defeat but losing a key player in the process.
Bailly has impressed since his summer move from Villarreal and limped off after 52 minutes with what Mourinho believes could be a long-term knee injury.
"He is injured and I am afraid he is badly injured," the United manager said
"In his knee, in the ligament area
He feels that it is really bad."
Bailly has played all but one of United's matches this season, winning the club's player of the month award for August.
The centre-back was named man of the match in three of their four matches that month and now potentially faces a substantial period out injured.
There are also concerns over Marouane Fellaini, who was caught by a nasty-looking David Luiz challenge in the second half.
The Chelsea defender was booked for the challenge and the Belgium midfielder was replaced at half-time.
Mourinho would not be drawn on whether the decision was fair and was coy when asked if Fellaini was injured by the challenge.
"If I'm going to say that he was injured, you are going to say again...," he said
"It was a bit of both (tactical and injury)."
United are back in action on Wednesday when Manchester City arrive in the EFL Cup, with a home match against Burnley following on Saturday.
Wayne Rooney looks a doubt for the upcoming matches after missing the Chelsea match with an unspecified training injury.
"Injured in training in the last session," Mourinho told Sky Sports of his captain's absence.
"He was so keen to play against Fenerbahce that he hid it and then he felt it in the training session and he couldn't come."
Source : PA
Source: PA