Franck Ribéry gave the Bundesliga outfit a first-half lead after 17 minutes, but Germany midfielder Mesut Ozil levelled for the visitors with a close-range finish.
Madrid appeared to have rescued a draw from a game dominated by Bayern but the home side scored a deserved winner in the dying moments, with the prolific Mario Gómez beating visiting goalkeeper Iker Casillas.
“We have the second leg to come and it’s not like we have to make a historical comeback, what we have to do is very achievable,” said Mourinho.
“If we win at home, we are there. I am optimistic we can return here to play in the final.
“I think a more justified result would have been a draw, but that’s football. Whoever scores goals wins games, simple as that.
“It’s not a bad result, it just means we have to win at home and turn it around.
“It wouldn’t be the biggest turn around in history, I still think the team can do it, the fans will be behind us, just like the fans helped Bayern.
“We will prepare after Saturday’s game and the team will be ready.”
Ribéry, who was denied a first-half penalty by English referee Howard Webb, produced a sharp finish to give Bayern the lead.
But the Madrid manager felt Webb made a mistake in awarding the goal – Ribéry’s shot narrowly missed his Bayern team-mate Luiz Gastavo, who was standing in an offside position en route to the net.
“We had the feeling that one team could get through with a lucky punch and they made it,” added Mourinho.
“Their first goal was offside, that is clear. I accept the referee’s decision, but he shouldn’t have given the goal.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news