The young Gers produced an irresistible attacking display and were propelled by goals from Max Cameron, Kyle Glasgow and a brace from Cormac Christie.
Speaking to RangersTV after the triumph, Smith said of the display: “It was excellent. When you see the draw and know it’s only the second round you know it could be a tough one.
“But the boys killed that with their enthusiasm, appetite to play the game, and to go compete.
“When you do that you give yourself the chance to show your quality and that’s what they done.
“When you come into a game like this as a coach you always worry about stuff like set-pieces, but they killed that with their aggression and intensity to go and press the ball.
“It was a really good performance all round.”
Cameron and Glasgow wreaked havoc on the flanks and were rewarded with fantastic long-range finishes in the second half.
Christie, meanwhile, scored either side of the half-time interval and led the line with distinction.
It was an all-round terrific display from the young Gers who will keen to maintain the standard set last night throughout the competition.
Smith added: “They [Cameron and Glasgow’s goals] were two outstanding finishes.
“As wide players you want them to be positive and go commit people, they continued to do that and both got their rewards. The two goals are outstanding.
“I’m pleased for [Christie] because he deserved it.
“He actually done a lot of the unselfish side of the game as well; we spoke to him yesterday about the tactical side and he applied that.
“He got his opportunities off the back and finished really well so he really deserved his goals.
“I don’t think we had to defend as much as we thought, but there was probably one big moment where Oliver Hynd makes a big block when we lose the ball in the middle of the pitch; even moments like that in cup ties are really important.
“I’m really pleased with the clean sheet.”
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