United, who trailed early on when goalkeeper Josh Perryman’s kick hit Crewe striker Luke Walley and looped into the net, dominated the contest at Bramall Lane and reached the second round thanks to goals from Jordan Hallam and George Cantrill’s injury-time winner.
And Geary, the former Blades favourite who now coaches the club’s U18s, said: “I thought we thoroughly deserved it. It was a big night for the players, at Bramall Lane in a competition all youth players aspire to play in.
“But I thought they managed the game well, especially after going behind to a soft goal early on. Your game plan more or less goes out of the window when that happens! But they grew back into the game, which isn’t easy after going behind so early.
“They ground it out and dominated the second half, with chance after chance, and sometimes you wonder if it’s going to go your way.
“So credit to the lads.”
Geary, who made 115 appearances for United after making the switch from Wednesday via a spell at Stockport, added: “They didn’t get disheartened and played like how I feel a Sheffield United team should play, with character and quality at times.
“I’m constantly on at them, reminding them how important mental strength is. We’re doing well, but the other team will sometimes go on top and it’s important not to panic.
“If you panic, you’ll make mistakes. You have to stay structured, believe in yourself; as a team and as an individual.
“Especially at Bramall Lane. Make the first team and go a goal down early, and you’ll have 20,000 people wanting to know how you’re going to sort it out.
“Ultimately, that’s the goal - to show kids how to play at this stadium and in front of that crowd. So it’s great for their development in that sense.
“At the time, I wasn’t happy to go a goal down but looking back, it was a great test and I have to give credit to every single one of the players.
“They’ve been outstanding since I’ve come back to the club, and have answered every question I’ve asked of them.”