Jordan Richardson's strike midway through the opening half earned the Potters their first points of their Barclays Under-21 Premier League Group 2 campaign in their fifth match.
When speaking exclusively to stokecityfc.com after the final whistle, Kevan admitted that they needed to acknowledge the moment after such a difficult start.
"We didn't really talk about the game much straight after, it was just a case of letting them enjoy it because they've had a tough baptism at this level," he said.
"Before the game, we looked at the team-sheet and it was probably a little bit more of a level playing field compared to some of the teams we've come up against.
"That gave the boys a little bit of self-belief - we felt they were capable of getting something, and although we had a little bit of luck along the way, we've managed to achieve that."
He also expressed his delight for Richardson, who, after being top scorer for the Under-18s from midfield last season, netted his first goal of this term - and past a goalkeeper with Champions League experience in Artur Boruc.
"No doubt we'll be hearing about that from Jordan!" laughed Kevan.
"He's capable of that, to be fair, and it was good to see him get on the scoresheet today.
"It's about getting him in the areas that will allow him to do that. He's been a little bit frustrated with his own form, and he'll be the first to admit that. The goal will do him the world of good."
The points were secured when Daniel Bachmann kept out a stoppage time penalty from Sam Hoskins after Jordan Keane was adjudged to have handled in the area, and Kevan praised the Austrian 'keeper.
"Danny's pulled off a great save, one of a number in the second-half," he added.
"For the penalty, I asked the referee after the game whether it was ball-to-hand or whether Jordan's stuck out a hand, and he said it was the latter. There didn't seem to be any debate from our boys.
"It was a real team effort though - we were very disciplined, kept our shape well and always looked a little threat. I'm very pleased for them."
The team are next action on Monday 8th October, when they welcome Sunderland to the Britannia Stadium (7.30pm).