"There were few clear-cut opportunities for either side. Fiorentina showed a quality in terms of possession of the ball that we struggled to match at times.
"But, credit to our players, they had to work extremely hard in the game and we did that again."
The closest Fiorentina came to breaking the deadlock was when Adrian Mutu drilled in a late effort from 30 yards, but the Romanian was denied by an excellent save from Neil Alexander.
The keeper, filling in for the injured Allen McGregor, won praise from Smith for proving his value to Rangers squad.
And, after a season of encouraging away performances, Smith believes the return trip to Florence on 1 May holds few fears.
"You gain a confidence in terms of playing in European games," Smith stated. "I felt that this season was going to be a bit early for us European-wise.
"But we've gained that and we're a difficult team to play against and certainly to score against.
"The away game, where the away goals are worth double, there's always a little edginess.
"We can take a bit of confidence from the away games we've played this season. If you look at the Champions League, we managed to score away from home in Lyon and Stuttgart and also at Lisbon and Panathinaikos.
"I don't think these are places anyone would relish to go to and having to win a game. But we've managed to go and score there."
They're going to have to come out and really have a go and it might open up for us
Neil Alexander
Goalkeeper Alexander was delighted to have kept a clean sheet on his European debut.
The 30-year-old, who has played the last three games in McGregor's absence, said: "I enjoyed it. It was always going to be a tough game, but give credit to our defence, I thought we were superb.
"They're a good team, a very, very good team. They've got some fantastic individuals.
"But I think we played well tonight and I think maybe they didn't reach their full potential."
"The away game's going to be a totally different game.
"They're going to have to come out and really have a go and it might open up for us.
"Our record in the away games has been fantastic. We know we can go there and score."
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