The loss to the Germans may not have been quite as emphatic, or humiliating, as the back-to-back 4-1 defeats to Sevilla and Unirea Urziceni in their other matches in Glasgow, but it was enough to render the final game in Spain as meaningless.
"We've not been good enough when the expectation level has been for us to go and win a game," admitted Smith.
"We haven't been good enough and we have to take that on board.
"There are no excuses from us. The home matches have all ended up in a similar fashion regardless of the systems we have played."
With Scotland's only representatives now out of the Champions League, Smith was asked how he felt their failings in the tournament reflected on Scottish football as a whole.
But he insisted: "I can't talk about Scottish football - I can only talk about Rangers.
"Some of the other teams might have acquitted themselves better in the Champions League, I don't know.
"I can't speak about the rest of them. From our own point of view we are extremely disappointed by the way we have played in our home games and that has been the biggest disappointment for us."
Kris Boyd was handed a rare start in the tournament and squandered a decent opportunity to haul Rangers back into the game but Smith refused to brand the moment as pivotal.
"We've had opportunities like that in all our home games," he said.
"We can't say that was a turning point in the game. It was a chance for us to get back into the game. It was there for us.
"But tonight's match was very similar to the previous two home matches we've had and that's been a problem.
"We've looked far more comfortable away from home than we have at home. Away from home, maybe the expectation is not as great in terms of having to go forward and win the game.
"Even our possession away from home has been better and that's been a disappointment for us."
Boyd also shrugged off his miss after the game.
He said: "That's football. These things happen. I would be more disappointed if the chances weren't coming.
"I didn't take them tonight but I'm sure that if they come again on Saturday against Aberdeen I look forward to putting them in the net.
"We have one game left, we go to Sevilla, it's going to be tough but you put that Rangers shirt on with pride and we need to go there and put on a show.
"We need to pick ourselves up and we have a chance to stretch our lead in the SPL on Saturday."
Smith did single out Allan McGregor for praise after he produced several excellent saves to prevent another heavy home defeat.
"He has been doing really well for us at the moment and his form is terrific," said Smith.
"If there is a better goalkeeper around, I've yet to see him. It's the one thing we know we have got and that's an exceptionally good goalie."
Smith opted to leave Madjid Bougherra on the bench after the defender returned late from international duty for the third time this season at the weekend.
But he did not regret the selection, saying: "It was a fairly straightforward decision to make."
The win - thanks to goals from Sebastian Rudy and Zdravko Kuzmanovic - resurrected Stuttgart's own campaign and delighted boss Markus Babbel's only complaint was that they did not leave Glasgow with a larger victory.
"It was a really good game," he said.
"I'm happy with the way we played. We were aggressive and we won our one-on-ones. The only hitch is that we could have scored more.
"Overall, I am happy and satisfied with the team. We had a good performance and it was very difficult for Rangers to create chances.
"I'm very proud of my team, they did a good job."