The Swiss side came from a goal behind to win 2-1 on Wednesday night, ending the Blues' 29-match unbeaten home run in Champions League group-stage matches.
Mourinho's men had been seen as hot favourites to qualify from a group which also includes Steaua Bucharest and Schalke but they now have work to do after the unexpected setback.
However, Mourinho said: "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.
"We lost three points that we must get somewhere. We must get them, (from) 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."
Mourinho insists he is happy with his striking options and says he is expecting improvement from new-boy Samuel Eto'o, who has arrived from Russian side Anzhi Makhachkala.
"The sharpness, that click to score, we have to wait," said Mourinho. "But he's a great player and he will score goals."