The striker believes his side's attacking style of football left Los Blancos stunned and says the win marks a great stride forward for the club.
The Poland international gifted Dortmund an early lead in the first-leg of their Champions League semifinal, before Cristiano Ronaldo leveled the scoring in the dying minutes of the first half. Dortmund stepped up its game after the break as Lewandowski netted three more to leave BVB on the brink of the Champions League final.
"We played really well in the second half and Real Madrid had no idea how to deal with us. We scored three goals and played unbelievably well," Lewandowski told Uefa.com. "It was almost perfect. Obviously I'm delighted because we won 4-1 and it was an outstanding performance, but we're not in the final yet.
"We've made great strides tonight, but we need to be alert from the very first minute in Madrid, because they're still very dangerous.
"We're a good team and we're not afraid of Real Madrid, but we're going to have to play very well over there."
Lewandowski, 24, has netted 10 goals in 11 Champions League appearances so far this term, trailing only Ronaldo, who has 12 goals.