The 17-year-old came into the starting eleven for fourth round Tunnock’s Caramel Wafer tie and it was the first time he had played in the competition.
He said
“It was a bit of a shock to me at first when I first found out I was starting but I just tried to get on with it and tried to do my best.
“Everyone is so together in there it is a great team to play in.
Budinauckas thanked goalkeeping coach Graeme Smith and Academy analyst George Brown for their research as he saved two penalties to send Rangers to the last eight.
He added: “George and Graeme Smith had looked at where they put them and the first one they managed to guide me the right way to save it.
“The supporters were brilliant tonight, I’d like to say thanks to them all for coming out and supporting us it really helped.”