Goals from Arturo Vidal, Mario Gotze and Robert Lewandowski earned the Bundesliga champions a 3-1 victory at the home of their fifth-tier opponents, yet Lahm has acknowledged that Pep Guardiola's men were by no means at their best.
"The most important thing is that we have progressed to the next round and that nobody got injured," the former Germany international was quoted as saying by Kicker.
"But it is clear that we will have to play better next time. Thank god we immediately scored a second goal after they equalised. You never know what can happen in football."
Bayern open their Bundesliga campaign at home against Hamburg on Friday, with HSV likely to be low on confidence after crashing out of the DFB-Pokal following a shock defeat to Carl Zeiss Jena.
Nevertheless, Lahm has warned his team-mates not to take the game lightly.
"Hamburg's Pokal exit will not affect Friday's game," the versatile defender added. "HSV will do everything within their powers to get off to a good start in the Bundesliga.
"It is up to us to ensure the three points remain in Munich."
