The Poland international striker bagged a brace as Dortmund triumphed 4-2 at Zenit in the first leg of their last 16 tie on Tuesday.
With a two-goal cushion to take back to Signal Iduna Park for the second leg on March 19, Jurgen Klopp's side are in a favourable position to take another step towards a second successive Champions League final.
But Lewandowski urged Dortmund to "take nothing for granted" and to once more show their superiority over their Russian opponents.
"It's a really important win, especially picking up four goals on the road, but conceding two hurts," he is quoted as saying by Bundesliga.com.
"We can't take anything for granted; we're not in the quarter-finals just yet. The pitch conditions made it very difficult but we were determined to win this match.
"It was a great performance, but we've got to show we're the better side in the second leg as well. We've got to keep performing and make sure we give a good account of ourselves with our fans behind us in Dortmund."
Forward Marco Reus was also among the scorers, notching Dortmund's second as they sailed into a 2-0 lead after just five minutes.
The Germany international believes Dortmund are well capable of seeing out the tie, and was delighted to bounce back from a disappointing 3-0 defeat to Hamburg in the Bundesliga at the weekend.
"We knew we hadn't played well against Hamburg, but we've got plenty of confidence," Reus commented.
"We took our first two chances clinically and executed the coach's game plan to perfection during the opening half-hour, although we should have put the game to bed earlier.
"We've got another game to go but we've put ourselves in a great position. I don't expect us to concede three at home."
