Joachim Low's side, already through to the 2010 FIFA World Cup South Africa™ thanks to their 1-0 win in Russia on Saturday, made a number of changes to their starting XI and the incoming players failed to shine.
Jonatan Johansson opened the scoring for Finland after 11 minutes and the visitors held out until the final minute, when Lukas Podolski scuffed home a scrambled equaliser.
Bayern Munich defender Lahm told ARD: "We always have trouble playing against teams that pack their defence, just as we did against Azerbaijan.
"And that was the case today as well. They scored the goal early and then played defensively."
The final whistle was greeted with boos at the Nordbank Arena and Lahm said he could understand the fans' discontent. "The fans pay to come into the stadium and see goals, and we couldn't do that," he said.