Pilkington netted the 60th-minute winner against the club he began his career at, extending the Canaries' unbeaten run in the league to six games.
The 24-year-old believes that Norwich's form has picked up due to a more clinical nature in front of goal, culminating in today's famous victory.
"We've been a bit more ruthless and we're putting our chances away; maybe we could have had another one at the end to make it a bit more comfortable," Pilkington told ESPN.
"It's a great day for Norwich and it's a massive win for us. We've been performing well over the last couple of weeks and we showed today that we could beat the team that is probably the best in the league."
The result lifts Norwich up to 13th in the Premier League table, while United are usurped at the top by rivals Manchester City.