The Ibrox club take on Zenit St Petersburg in the final at the City of Manchester Stadium tonight.
Rangers remain on course for a quadruple, with the UEFA Cup now arguably the most attractive of the trophies still up for grabs.
Smith freely adm
its to being surprised by his side's enduring continental campaign but having overcome Panathinaikos, Werder Bremen, Sporting Lisbon and Fiorentina to reach their first European final in 36 years the Rangers boss is looking for one last push from his players.
"Once you reach the quarter-final stage, you start to think about the final and realise just how much it means to everyone," he said.
"It starts to take over everything else and it has done for the last few days. The European competition isn't one that we thought we would get this far in so it's a nice surprise."
Zenit overcame Bayern Munich in their semi-final with an emphatic 5-1 aggregate victory and, as far as Smith is concerned, that means Dick Advocaat's men are favourites to claim the trophy.
"It's difficult to try to assess a team until you have to play them," he said.
"But you only have to look at the semi-finals. The 1-1 draw in Munich was a terrific result for them and to win 4-0 at home was probably one of the best results in all the European competitions this year. It will be a very, very tough night for us."
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