The Bundesliga outfit impressed with a fine performance at Signal Iduna Park, but the Germany international believes they are not in the final just yet
The centre-back has admitted that BVB are in a good position to make it to the final after their first-leg win, but has insisted that Madrid cannot be written off just yet.
"It's a superb result, obviously, but Real Madrid are even stronger at home. They're going to come at us for 90 minutes and we're going to have to defend against that," Hummels was quoted as saying on the official Uefa website.
"It's going to be the most difficult match of our careers so far, but if we can survive that test, we can all be very proud and that is, of course, our aim.
"We're in a great position now, but to say we've got one foot in the final is way over the top. Bayern are sure to complete the job, and we hope to do the same."
The centre-back was at fault for Cristiano Ronaldo's equaliser, but he was pleased with the way BVB bounced back after the break.
"I think we can be tremendously proud of the team's performance tonight. The way we played was a measure of the players and I'm all the more delighted at how the team reacted to my mistake. The way we dealt with it and what we showed subsequently was fantastic."
The return leg takes place at the Santiago Bernabeu on April 30.