After going down to an early strike from Augustine Mulenga, United rallied back through and Evans Rusike before Gladwin Shitolo equalised for the Buccaneers.
The clash eventually went to a penalty shoot-out, where the Pretoria outfit triumphed 4-3.
“I think early on, we allowed Pirates too much pressure and time on the ball. We showed them too much respect. I think the goal changed that for us," Furman told SuperSport TV.
“It showed that we have nothing really to fear. For long periods, obviously Pirates dominated. We lost our legs at the back, but we had to hang on and we put in a solid shift in defence,” Furman said after the game.
The Bafana Bafana international also reserved special praise for new signing Ghampani Lungu, who made his full debut on the night.
“I got to give special mention to our young right back Jones. Came in for us, Jones is his nickname. He is a striker/winger. We had a bit of a problem at right-back. He came in and was absolutely outstanding," he added.
“So from him to all the boys, I think everyone put in an outstanding effort. We delighted to go to the next round and we’re looking to defend our trophy."