The Light Blues left it late to break down a stubborn Jambos side, with substitute Chris Eadie stroking home with 15 minutes remaining.
Speaking to RangersTV after the triumph, the Gers Under-18s head coach commented: “The performance probably wasn’t at the level that we expected it to be, but we knew the game was going to be tough.
“We mentioned that the game wasn’t going to be pretty; Hearts are a good team at this age group.
“We always knew we were going to need everyone, including the substitutes. And, again, credit to the boys who came onto the pitch because they were ready to play.
“I know some of them were disappointed that they never started, which is natural and a part of football, but one thing you need to do is make sure you’re ready to have that impact and all of them did.
“We got a little bit panicky towards the last 15 minutes, but that’s understandable because they were putting balls into our penalty box, loading numbers forward. But we handled that really well.”
The victory moves Rangers into the semi-finals of a competition that they have reached the final of in the previous three editions.
And Smith says his current crop of players are motivated to get their hands on silverware this term.
He added: “One of the things about the Youth Cup is that we know we’re here to win it, which means we have our best players who are fit and available.
“We used them all and some players are going to be disappointed, but you need to learn to handle that because it’s part and parcel of being at a big club where there’s competition for places.
“I spoke to them before the game and I knew they were upset and that there was a bit of rage, which is fine, but as I said, when you come on the pitch you need to be ready, and all of them were.”