The Scottish side were second-best on the night as their attempt to add the European trophy to the League Cup they have already won and the league title and Scottish FA Cup they hope to secure failed.
Second-half goals by Igor Denisov and Konstantin Zyrianov proved to be enough to sink a tired Gers side that will now have to lift themselves for an extremely busy last week to the season.
After failing to progress from the Champions League group stage, Rangers had seen off Panathinaikos, Werder Bremen, Sporting Lisbon and Fiorentina to reach their first European final since 1972.
Their hopes of beating the Russian side, managed by former Gers boss Dick Advocaat, were boosted by the competition's top-scorer, Pavel Pogrebnyak, being suspended after his yellow card in the closing stages of Zenit's amazing 4-0 semi-final second leg success against Bayern Munich.
Smith decided to start with Jean-Claude Darcheville as the only recognised striker in his starting line-up and it was Zenit that created the first opening when Andrei Arshavin could only guide his shot in to the side-netting.
Anatoliy Tymoschuk tried his luck from distance but Neil Alexander was equal to the ambitious effort while at the other end Darcheville almost teed up Barry Ferguson inside the area only for Radek Sirl to take the ball off the former Blackburn man's toe.
Zenit appeared to be the more cultured side while the Gers were happy to soak up the pressure and hope to catch their opponents on the break.
In the 29th minute Aleksandr Anyukov forced Alexander to make a smart save after lashing a stinging shot towards goal but neither keeper was called on to make a really difficult stop in the first half.
Zenit should have had a penalty on the stroke of half-time when the ball clearly hit Kirk Broadfoot's hand inside the area but the referee waved play on.
The match opened up in the second period and Rangers thought they should have had a penalty for handball themselves when the ball struck Denisov, but again the referee was unimpressed.
The deadlock was almost broken in the 65th minute when a big hoof out of defence found the outstanding Andrei Arshavin.
Alexander came racing out of his area only for Arshavin to round him and fire a curling long-range effort towards goal only for it to be cleared off the line by the back-tracking Sasa Papac.
Zenit did score seven minutes later though when a simple Arshavin pass dissected the Rangers defence and Denisov kept his cool before slotting the ball past Alexander.
The Scottish side had nothing left although substitute Nacho Novo blasted a late chance over the bar before, with virtually the last touch of the match, Fatih Tekke squared the ball to Zyrianov who side-footed the ball into an empty net.