The 17-year-old goalkeeper produced a string of impressive stops to repel Hearts’ advances after the young Gers broke the deadlock through Chris Eadie with a quarter of an hour remaining.
Speaking to the official Rangers website, the Northern Irishman commented: “It was a good, solid performance in tough conditions.
“The opposition threw everything at us, especially towards the end after we got the goal. But we done well to keep it tight, and it’s a good thing on my behalf to get the clean sheet.
“Stevie [Smith] said it was going to be a tough game, so we all had to be together. It was about giving everything that we had.
“I think the boys showed that from the first whistle to the last. Obviously, Leyton Grant’s blocks and I made a couple of stops myself, so we all had to show good heart.”
The Light Blues will await confirmation of their semi-final opponents, with the side now one step away from a return to the national stadium.
Munn says he’s hungry to play his part in the side’s journey after getting a taste of the competition on the substitutes bench as a 16-year-old last season.
He added: “It’s massive for me on a personal note, because I missed out last year in the Youth Cup. It was a relief for myself and the team to get the goal [to take us through].
“The next game is massive for everyone, especially if we can get to Hampden again.
“There is always the expectation that Rangers need to get to the final. I feel that the boys are used to it; we’ll give it everything that we have to get to Hampden, and hopefully go on and win it.”