Rangers hit the Ayrshire side for four, propelled by a first-half brace from 15-year-old Kyle Glasgow.
Springing from the substitutes bench in the second period was also fellow youngsters Luca Rankin, who teed up Cameron Fernie, and Chris Condy, who capped off a flowing move for the fourth.
Speaking to RangersTV after the triumph, Smith commented: "Kyle Glasgow puts himself in really good positions at the edge of the penalty box, and when he gets in those positions, we know he has that quality to finish.
"Ashton Scally was involved in three out of the four goals, so I'm pleased the young players contributed to the end product.
"Chris Condy comes on and gets himself a goal, which he deserved because his movement was good.
"He has deserved an opportunity, and whether it's five or 55 minutes, you need to go and take it.
"We can trust them, but we also need to understand they're going to struggle as well.
"When you go to Under-19s it's quite a big jump from Under-16s, but even the boys out on loan they're still going to contribute in our Under-19s group too.
The Gers fell behind early in the contest but were soon ahead when Glasgow struck twice before the half-time interval.
Killie, coached by former Rangers Academy graduate Chris Burke, continued to push in the second half, but the Light Blues showed their quality in putting the game beyond the visitors through Fernie and Condy's contribution.
Smith said of the display: "I don't think it was a 4-1 game. Kilmarnock would have been disappointed at half-time that they went in losing because I thought they were probably better than us in the first half.
"We had a few issues out of possession which we struggled with, but it was good to get them in at half-time when they were winning to help get that message across. I thought we improved a lot in the second half.
"We also knew we were going to struggle because the personnel we had felt like a new group.
"I enjoyed the freshness they brought and the character after going a goal down to get back in the lead at half-time, but I told them after the game they need to enjoy winning while also understanding that there are things as a group we need to get better at.
"The third goal helped us and killed the game because the spaces became bigger. We looked a real threat in transition, but to get to that point after the struggles we had in the first half was a real positive."
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