Rangers improved after the break but failed to put the Sporting defence under enough pressure, as first Jean-Claude Darcheville and then his replacement Nacho Novo toiled with little support in the lone striker role.
The home side tired towards the end of a physically draining encounter, with their recent hectic fixture schedule appearing to catch up with them.
In the final five minutes, Sporting almost snatched a priceless away goal, with efforts from Liedson and Tonel going close.
"I don't think it was physical tiredness in the last 15 minutes, I think it was a mental thing," explained Smith.
We are more than capable of going there and scoring
"Mentally we had one or two errors that caused us a few anxious moments but at the end of the day we can't disagree with the result.
"There were very few opportunities for either side throughout the game."
Rangers midfielder Lee McCulloch said the Ibrox club remained favourites to progress to the last four.
"The ball is still in our court. We would liked to have scored. But it's not the end of the world, and we won't let our heads go down," he said.
"We didn't play well, and there was a lot of route-one football. But we didn't concede - and that is the positive thing.
"We are more than capable of going there and scoring, so that's why we will be confident."
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