The Gers managed a 2-2 draw in Lisbon and after a 1-1 draw in the first-leg, Rangers went through to the last 16 on away goals.
Maurice Edu slid home the equaliser in the final minute of the game in Lisbon last night.
“We are obviously pleased to get through,” Smith said on Sky Sports News.
“I felt we started slowly but then we managed to get a goal through El-Hadji Diouf. Sporting were the better side for the remainder of the first half and got a goal back.
“There was not much between the sides in the second half but the away goals rule worked in our favour.
“There were very opportunities in the game and we were disappointed with the goal we lost. With our height at the back we should have handled it better when the ball came in but it broke to the edge of the box and gave Sporting their equaliser.
“We lost another one in the second half but we came back again at the death to go through so the lads deserve a lot of credit.”