The Poland international scored all his team's goals in a 4-1 win over the nine-times champions in their Champions League semi-final first leg.
"In the second half Real Madrid did not know how they should play, at some moments they were helpless," Lewandowski told the Polish pay-TV platform nc+. "We took the first step [towards the final].
"I felt confident, but there were even better matches. My efficiency was almost 100 percent but there were matches when I did more for the game," he added, before dedicating his goals to his late father.
Speculation surrounds the 24-year-old's future as he has refused to sign a contract extension beyond 2014 and has kept quiet about his plans.
"I do not have the feeling that Robert is on the run and we are not the ones to send him away," his manager Jurgen Klopp told reporters.
"Let's wait and see what happens next."
Dortmund officials also remain optimistic of keeping him.
"Robert has a contract until 2014 and there is no exit clause like with Mario Gotze," said club boss Hans-Joachim Watzke.
"It is our explicit wish to keep him until 2014. That is why we are saying no to a transfer fee."
Former Poland international Zbigniew Boniek lavished praise on his compatriot, who became the first player to score four goals in a Champions League semi-final.
"I hand over Lewy the title of 'bello di notte' (beauty of the night)," Boniek, now head of the Polish Football Association and the only Polish outfield player to have won the European Cup, said on Twitter.
Juventus president Gianni Agnelli handed Boniek the cryptic nickname because of his performances in evening matches in the 1980s.
Dortmund's dazzling performance came a day after Bayern Munich crushed Barcelona 4-0 in the other semi-final first leg, raising the prospect of an all-German clash in next month's final at Wembley.
