The striker hopes to lead BVB to as many trophies as possible before leaving for Bayern Munich in the summer.
The Poland international hit a second-half double, after Marco Reus and Henrikh Mkhitaryan had secured an early lead in Russia, to put BVB in full control of its Champions League last-16 tie with Luciano Spalletti's men.
Lewandowski is set to join Bayern Munich in the summer when his contract at Signal Iduna Park expires, but he says that Tuesday's goals will not be his last in Schwarzgelben colors.
"Of course I'm satisfied with the game, with the result and my two goals. But the last word has not been spoken. That was not my last goal," the forward told the club's official website. "We'll continue to play in the Champions League and I hope to score a few more."
Lewandowski went on to warn his side not to allow complacency to creep into its game in the second leg, after Zenit almost forced its way back into the match in the second half with goals from Oleg Shatov and Hulk.
"The coach [Jurgen Klopp] is right when he says we're not yet in the next round, even though we won 4-2. We must show we are the better team in the second leg, too," he said. "In the first half, Zenit had no opportunities to score, while in contrast we had a good start with two goals in the first five minutes. But I think we could have played better in the second half, since we made too many mistakes.
"The fourth goal was very important — at 3-2, Zenit could believe they could get a draw. Away goals count double in certain cases, as with the game between Bayern and Arsenal last year. We still have important games in the Bundesliga, the cup and Champions League. I want to win as many as possible. It doesn't matter that I'm going away after the season ends."