The 17-year-old midfielder dispatched the winning spot-kick to send his side to next month's final and move one step closer to potential silverware this campaign.
Speaking to RangersTV, the teenager commented: "The boys were unbelievable. We were confident on penalties and we practiced them yesterday, and most of them went in.
"It's good that we're back to Hampden again and we're all buzzing.
"I'm normally confident with my penalties, and I just thought to myself to pick my spot and place it. And fortunately it went in."
It was a tale of two halves for the young Gers as they found the leveller moments into the second period after falling behind on the stroke of the interval.
Curtis, however, believes the better team came out on top in the end, and the midfielder is now targeting glory in next month's final.
He added: "I thought it was credit to Dundee United as they created chances and took one in the first half.
"We had a lot of chances in the first half as well, but we didn't take them.
"Luckily Chris [Eadie] scored to make it 1-1, and we're all delighted to go to Hampden again.
"I think we're all confident in each other, and even the boys who came on done very well.
"It's my last year at this level, so I just want to go on and win it."