The German side nearly paid the price for missing several chances at the Bernabeu but held on for a 4-3 aggregate win despite losing 2-0 after conceding late goals on Tuesday and could feature in an all-German showpiece at Wembley on May 25.
"I don't care who we play in the final, I relish the challenge of facing either Bayern Munich or Barcelona in London because it will be by some way the biggest game of my career," the 24-year-old Serbia international told Reuters.
With a 4-1 first-leg lead, Dortmund seemed to be cruising until Karim Benzema struck in the 83rd minute and Sergio Ramos scored five minutes later to set up a frantic finish.
"We lost our focus in the last 10 minutes and we were also lucky not to fall behind on the night in the opening quarter of an hour but overall I think we deserved our 4-3 aggregate win," said Subotic.
"We should have put at least one away when it was 0-0 here and that would have definitely sealed the tie but in the end we are in the final and it's all that matters," he added.
The centre-back, who hardly put a foot wrong before Dortmund were rattled and forced to hang on by their fingernails against Jose Mourinho's side, said his team's industrious approach paid off against the nine-time European Cup winners.
"We may not be the most entertaining team in the world but there is nowhere I would rather play because this is a hard-working outfit where players put their bodies on the line for each other.
"We always knew Real were a classy outfit who could move the ball around seamlessly but although they had more chances... we had the better chances to score."
This season's Bundesliga champions Bayern carry a 4-0 first-leg lead into their semi-final return against Barcelona at the Nou Camp on Wednesday as they chase a treble.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.