Jean-Claude Darcheville secured three crucial points when he grabbed the winner from the penalty spot after Charlie Adam had returned from his first-team exile to cancel out Mario Gomez's opener at Ibrox.
Perennial French champions Lyon and the might of Barcelona also await Rangers in Group E and, asked whether tonight's result would make their other opponents sit up and take notice, Smith said: "I don't know, maybe if we continue to get results like that.
"We need to continue to play our way and hope we are good enough to take more points. We need to go away from home against exceptional teams and that's a big test for us overall.
"We are working hard at the present moment and Scottish teams are proving difficult to beat for other countries. We hope that continues but we are in an extremely tough group and we need to play to a high level to achieve anything at all.
"We don't have a lot of players with Champions League experience and we started slowly against Stuttgart, who were the better team in the first period.
"We were disappointed to lose the goal when we did because we were starting to get into the game. But, in fairness, the players didn't let it affect them and got back into the game. We are delighted to win the match."
He added: "Any win is important whether at home or away, that's an important factor in this group."