The sides meet at Signal Iduna Park on Tuesday for the second leg of their quarter-final, with goals from Gareth Bale, Isco and Cristiano Ronaldo last week having put Real in control.
Although Dortmund, who knocked out Real en route to last season's Champions League final, clearly face an uphill task to progress, Carvajal is not taking Jurgen Klopp's men lightly.
The 22-year-old feels defensive solidity will be crucial if Real are to reach the semi-finals, but is also hoping his team can add to their aggregate lead.
"In the first leg they (Dortmund) had chances and the defence will be key (on Tuesday), but we won't go out and sit back. We'll try and take the lead in the first half an hour," said Carvajal.
"It's a very important match and we'll approach it with verve and the intention of winning to get to the semi-finals."
Dortmund's progression last season was all but sealed by a stunning 4-1 home win in the first leg, with Robert Lewandowski scoring all the hosts' goals.
Carvajal is expecting a stern test this time around as Lewandowski returns from suspension.
"This is practically a final. The lead from the first leg is big, but not conclusive," he added.
"They are going to come out and give their all and we are going to try and win and not speculate.
"This stadium puts pressure on you and the first 15 or 20 minutes will be crucial because they'll be lifted by their fans and will try to score and put pressure on the tie."
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