The young Gers ran out 2-1 winners over Partick Thistle thanks to first-half goals from Callum Burnside and Chris Eadie.
In doing so, the Light Blues set up a third successive Old Firm final showdown in the competition after Celtic overcame Clyde in the corresponding last-four clash.
Speaking to RangersTV after the triumph, Smith commented: “I just said to the players there that I absolutely loved the game. It felt like a proper game.
“We showed real quality in the first half and, in the second half, we had to dig in a little bit and suffer.
“We lost the goal to go 2-1 and it can become a bit nervy, but I thought we managed the game excellently.
“There were so many things in the game that I’m happy with.
“The first half was full of [quality]. I spoke to them before the game about their mentality.
“They put the three things together and produced a really good performance.”
Among the visitors’ side this evening were Sean Kelly and Steven Lawless, the latter of whom has featured over 200 times for Thistle at first-team level.
Indeed, the Jags produced a much improved second half showing to reduce the arrears, asking questions of a young Gers side who dug deep to seal their passage to the final.
Smith added: “We knew [a response] was probably coming.
“In the first half I thought we dominated and we showed quality, but we knew there was going to be a reaction from Partick Thistle.
“They changed shape again and went direct with quality, which caused us a few problems.
“I’m not someone who really focuses on age or team sheets.
“I think the players noticed they were up against some experienced players, and they had Steven Lawless at the top end of the pitch who I played against.
“It’s a test for them, but no matter who they’re playing against or their age, I expect them to go and compete and show their quality.”
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