After Elias Sørensen gave United a first-half lead with his 18th goal of the season on Tuesday night, Sol Campbell's Macclesfield levelled with five minutes remaining at St. James' Park through a Scott Wilson chip.
With the game heading straight to penalties, goalkeeper Harker superbly pushed away Ben Stephens' spot kick before Mo Sangare sealed the Magpies' spot in the last 16 after five perfect penalties from United's second string.
After carrying out penalty research with goalkeeping coach Steve Harper before the game, Harker admitted Stephens was not one of the Macclesfield players he had analysed in the build-up.
"Before the game, we had done research on the penalty takers but they only had two on the pitch for the shoot-out," Harker told nufc.co.uk.
"(Stephens) was not one of those players so it was just down to instinct and it was enough to see us progress.
"Thankfully, we were ready and did our research and I'm absolutely buzzing to qualify for the next round.
"It wasn't how we wanted to do it and how we got through does not mask the way we played but we got through and that's all that matters."
With United's youngsters now three wins away from the final - which will take place at Wembley Stadium - the 20-year-old is keen for his side to advance further in the competition whilst continuing to gain experience in the early stages of his career.
Harker added: "It would mean a lot to go further into the competition. I haven't had as many opportunities to play in the past six months.
"The game was massive for myself and felt like my Champions League, especially coming to St. James' Park. The atmosphere was amazing and the fans were ridiculously loud which meant a lot to me.
"When I saved the penalty, the noise from the supporters was incredible. I have dived past the ball which nearly span over my body. I clawed it away in desperation and managed to keep it out of the net, so I'm delighted."