Goals from Jack Nardiello (2), James Alabi and Kris Scott sent the Potters cruising through on a memorable night for the youngsters at the American Express Stadium.
Perkins believes the organised and disciplined nature of the performance reflected Stoke City's football philosophy perfectly, and believes it's all down to teamwork.
"It was a complete team performance. I think it represented Stoke City and what we stand for," he said.
"It wasn't so much about outstanding individuals, but collectively it was excellent. That's what the Club is about: work-rate and commitment."
"It was a long day, but they prepared themselves very well with the support of all the staff as well. They're contributed massively."
Perkins was proud of how the players, seven of whom were first-year scholars, responded to playing in a professional stadium, saying they rose to the occasion when it mattered.
"With young players you never know how it's going to happen. Sometimes on the big stage they really falter, but everyone stepped up to the mark," he added.
"We're quite a young team but the spirit was outstanding so great credit to them. It's been a collective effort by everybody, though, and they've represented the club magnificently."
Scott's goal, the team's fourth and a superb lob from 35 yards, capped the night off perfectly.
"It was a tremendous goal from Kris, he saw the goalkeeper off his line and that's what he's capable of doing," said Perkins.
"I've been in the FA Youth Cup many, many years, and what it does do is that it gives them a little bit more to cling onto, especially going into the Christmas break now.
"They can get away and enjoy their break, and look forward to the next challenge."