The result means that Dortmund could progress with a goalless draw, but the Poland international believes that targeting a stalemate could be risky.
"Donetsk scored twice against us in the first leg and they showed how dangerous they are," Lewandowski told Bundesliga.com. "We can't play for a draw, or aim to get a 0-0 or 1-1. That would be far too dangerous.
"We desperately want to win it, even if it's not going to be easy. We know that we can score against Donetsk because we showed that in the first leg, and we should also get at least one goal on Tuesday.
"We're at home after all, so we've got to be positive. We want to, and have to, get into the next round and that is the clear objective on Tuesday."
Dortmund host Shakhtar at the Westfalenstadion on Tuesday.