Rangers lost 1-0 on the night to a second half strike from Diego and had to withstand serious pressure as the game wore on. Werder amassed 42 shots and 18 corners but failed to breach the Rangers rearguard a second time to take the tie into extra-time.
"It was a fantastic performance," Smith told BBC Scotland.
"I knew Werder Bremen would put us under pressure and they certainly did that. We've got a great deal of resilience.
You've got to give credit to Bremen. We had a little bit of luck at times, but we're just delighted to get through."
Smith also praised Alan McGregor who produced a string of outstanding saves to keep Werder at bay.
"Our goalkeeper was equal to anything - brilliant in fact.
"In the 15 months that I’ve been here he’s done exceptionally well."