Six years to the day since his most recent Champions League match as Chelsea boss, a draw with Rosenberg which marked the end of his first spell in charge, Mourinho's men followed up defeat at Everton by falling victim to the Swiss side's first win in England at the 11th attempt.
Goals from Mohamed Salah and Marco Streller, after Oscar had put Chelsea in front, also saw Basel end the Blues' 13-match unbeaten run at home in European competition.
Next on October 1 Chelsea play at Steaua Bucharest, who beat them in Romania earlier this year, before two matches with Schalke, as the 2012 European champions bid to avoid a second successive season featuring a premature end to their Champions League campaign.
"When we lose, I am the responsible (one)," said Mourinho, who did not see onlooking Chelsea owner Roman Abramovich in the immediate aftermath of the defeat.
"We lost three points that we must get somewhere. We must get them, (in) Basle, or Schalke, or Bucharest, or all of them or some of them.
"Normally you have to win the matches at home and get a few points away.
"Now we must win six points at home, Schalke and Steaua, but we have also to win points away. Probably we have to go to win at Basle to compensate for the defeat today.
"But the objective of finishing in the top two in the group phase and to go to the next stage of the Champions League is an objective that is not lost, far from it.
"It's an objective we're going to fight for and it's an objective that I believe very, very much that we're going to achieve."
Chelsea suffered the ignominy of becoming the first holders to exit the tournament at the group stage last term, but had not lost in almost 10 years and in 29 matches at home in the group stages.
The last time Chelsea lost at Stamford Bridge in the first stage was against Besiktas on October 1, 2003, and Basel thoroughly merited being the team who brought the run to an end.
Mourinho bemoaned the defending which contributed to the winner for Basel , beaten by Chelsea en route to the Blues' Europa League win last season.
Streller evaded the attentions of Samuel Eto'o and Gary Cahill to head substitute Matias Delgado's corner in at the near post. Petr Cech might have done better, too.
"The second goal is the kind of goal that is very difficult to accept," Mourinho said.
"We work very much on the organisation in defensive set-pieces and the header is in a position where we have two players defending that zone, plus the man that was marking Streller.
"Three players make a mistake and we were punished because of that."
Mourinho felt his side were fortunate to take an interval lead through Oscar's well-worked strike and crumbled when Salah struck 19 minutes from time.
"When the first negative moment arrives, which is the equaliser, the team shakes a little bit," Mourinho said.
Mourinho has placed emphasis on youth, even though his team has enormous experience, including Eto'o, who was ineffective.
Mourinho stressed his happiness with his strike options, after leaving Fernando Torres out of the squad and bringing Demba Ba off the bench, but admitted Cameroon forward Eto'o may be lacking the sharpness exhibited for Barcelona and Inter Milan after a spell in Russia with Anzhi Makhachkala, where he commanded a vast salary.
"When you are three, two and a half years in a place that doesn't motivate you, that you are out of the big stage, maybe you are there not for the right reasons, and you lose the hunger, the appetite," Mourinho said.
"Now he (Eto'o) has that back, he has that motivation, he wants to succeed, he wants to play, he's happy to be at this level. The sharpness, that click to score, we have to wait. But he's a great player and he will score goals."
Basle boss Murat Yakin refused to get too far ahead of himself after victory.
"For us, it's a great honour to win here," he said.
"We can enjoy the moment. It's not every day you can come from behind and win at Chelsea.
"Of course it's a great achievement. (But) this is one game, we've got five games ahead of us.
"There's a lot ahead of us still."
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