Oscar put the home side ahead but Mohamed Salah equalised for Basel and Marco Streller headed in a late winner.
“When we lose I don’t speak about the players or individuals, I speak about my responsibility,” said Mourinho. “I am responsible.”
Chelsea became the first Champions League holders to be eliminated at the group stage last season, must also play German side Schalke and Romanian champions Steaua Bucharest.
“We lost three points that we must get somewhere,” said Mourinho. “We must get them, in Basel, 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 Basel 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.”