The German pointed out that his team claimed more possession than the Spaniards and said he is optimistic about their prospects for the second leg.
"We were missing a little bit of luck. The decisive action was missing. We were in control and we wanted to win. You could see that for 90 minutes," Lahm told Sky Sports News.
"We had several good chances to score the important away goal, but it was not meant to be."
He added: "It is nice to come to Madrid and dictate the game here. I don't remember Bayern Munich dominating here like this before. Of course we wished for a better result. But we still can do this at home."
The two teams will meet in Germany for the second leg on April 29.