It was their first away win over the Potters after six defeats and three draws in previous visits.
Manager Jewell was delighted with the way his players responded to playing their second game in three days.
He said: "We did ask Stoke to put the game back a day but I wasn't surprised when the answer of 'no' came back and perhaps they wish they had now.
"I think it is testament to the players' fitness and attitude that they played two high tempo games in three days and came away with six points and two clean sheets.
"We have a belief we can win every game and that's not surprising when we've gone 17 games unbeaten.
"Of course that's not going to happen but we have that belief and long may it continue."
Jewell admitted the game looked to be heading for a stalemate until McCulloch's late strike.
He said: "There's always more then one way to skin a cat and I thought we just about edged a very tight and physical game.
"There was plenty of honesty from both sets of players, although not a great deal of football was played because it was a fast tempo game.
"Sometimes a 1-0 victory away from home gives me as much pleasure as a 5-0 win.
"We dug in there, restricting Stoke to very few chances after they had flown out of the traps in the first 10 or 15 minutes.
"As the game went on, I was thinking that a point at Stoke wasn't a bad result as it's never an easy place to go.
"Arguably this was one of the most physical games we'll play this season and I was pleased with how we coped.
"Then up popped Lee with the winner. He'd missed a good chance in the first half when he lashed at a shot so perhaps he owed us this one.
"It was a nice move and once he'd hit it, the ball zipped off the ground and you knew it was going in.
"During the game we carved out the better chances, Lee missed one, Jason Roberts missed a header while Alan Mahon hit the post."
Jewell also praised his side's defensive qualities, with centre-backs Matt Jackson and Ian Breckin getting a deserved pat on the back.
He said: "Our two central defenders were magnificent and are our unsung heroes.
"As a defensive unit, the whole team was very good and we got blocks in when it mattered to stop them."
Nathan Ellington was taken off in the last 10 minutes after taking a bang in the ribs.
But Jewell is hopeful the top scorer won't be adding to his name to a list of casualties which has reduced his squad to the bare minimum.
He said: "Duke got a bang on the side but hopefully he should be okay for Plymouth on Saturday.
"It was a fair old battle between him and Gerry Taggart out there, and I thought Gerry handled him very well."
Matchwinner McCulloch said: "With five or 10 minutes to go, we would have taken a point so I was delighted with all three.
"I remember David Graham laying the ball off to me, I just swung my foot at it and luckily it went in.
"It was good to see it hitting the net."