"We don't need any crazy result in the return leg, we can win with a normal result and go through," he said at the post-match press conference.
"I think my team can respond to this game, with our fans behind us."
Mesut Ozil, who brought Real level early in the second half, shares his coach's optimism that the tie is still wide open.
"I think that we will win the return leg," he said. "We are a touch stronger at home.
"We believe in our strength and I am convinced that we will go through.
"We will be coming back to Munich again."
Bayern Munich coach Jupp Heynckes believes his side did exactly what he had asked of them following their 2-1 win over Real Madrid in the Champions League semi-final first leg.
Heynckes wanted to see a reaction from his side after they effectively lost the Bundesliga title in their last two games, and he believes he got it.
"My players showed what I had demanded from them yesterday: lust and hunger for success," he told Sky television.
"I think we more than deserved the win because we played cleverly and intelligently."
The result was nevertheless disappointing for Real, but Mourinho did not want to dwell on Bayern's first goal, which could have been ruled out for offside against of Luiz Gustavo just in front of Iker Casillas.
"I don't want to criticise the referee," he said. "I will just accept his decision, even if it (the goal) should have been ruled out."
Heynckes also admitted that "similar goals have been ruled out in the past", but destiny wanted Bayern to win, according to their chairman Karl-Heinz Rummenigge.
"It was an emotional game and Real showed that they are a great side," he said.
"Fortunately, we had luck on our side in the end."