The Gers were humbled 4-1 by Unirea at Ibrox two weeks ago and Smith gave credit to his players for a much-improved showing.
He told Sky Sports: "It was a very good performance and we more than made amends for the last game.
"It was really disappointing to give away a goal so late in the game. Victory would have put us back into at least having an opportunity to qualify."
The Gers boss felt his side had done enough to claim the three points that would have taken them above Stuttgart and into third place in the group.
"They're always dangerous from set plays but outside of that they had maybe one or two chances, but we had far more and I felt we deserved to win the game," he continued.
"It's going to be far more difficult now but we just have to hope we can get ourselves together. We can put pressure on by winning our home games."
Rangers face Stuttgart at Ibrox on November 24 before travelling to Sevilla on December 9.