The 25-year-old, who netted twice in the 3-0 victory over Marseille, believes that the French side stood little chance of leaving with a result
The Poland international was on target twice in a routing of Elie Baup's men at Signal Iduna Park, as last season's runners up collected their first victory of the new European campaign.
"The team played well defensively, but Marseille had no chance," Lewandowski, 25, told reporters.
"We could have scored two more, but that does not matter. What is important is that we have our first three points in the Champions League this season.
"Now we must put our foot on the gas because we will not get far with three points from two games."
Jurgen Klopp's side, who slumped to defeat to Napoli in gameweek one, sit three points behind leaders Arsenal in Group F and Nuri Sahin anticipates a hugely competitive fight with the Gunners and the Partenopei for last 16 progression.
"You have to win home games in the group stage of the Champions League, which will give you nine points," the former Real Madrid midfielder added.
"Arsenal and Napoli are both really very good, but we not without quality ourselves and it will be a tough fit to the end, but that's the Champions League."
Dortmund resume their domestic duties with a visit to Borussia Monchengladbach on Saturday.