"It's a fantastic result for us. We were totally professional throughout. We didn't get sloppy or careless. Everybody was right on it," he said.
"At 3-0, there's a danger that you think the job is done and you lose that bit of an edge. But we didn't."
Wednesday took an early lead as Hartlepool's Paul Murray swept the ball into his own net.
Giles Coke doubled the advantage when he sent Gary Teale's cross into the bottom corner.
Neil Mellor, a handful throughout, made it three before the break when he beat the offside trap and swept the ball home.
Hartlepool barely troubled Owls goalkeeper Nicky Weaver other than a spectacular volley from ex-Rotherham winger Andy Monkhouse.
With 20 minutes to go, Mellor was brought down as he rounded goalkeeper Scott Flinders, who was sent the wrong way from the spot by Marcus Tudgay, who could well have been making his farewell appearance as the tranfer deadline looms.
Substitute Clinton Morrison added a fifth in stoppage time and is in contention to start Wednesday night's JP Trophy game with Notts County.
Hartlepool United: Flinders; Haslam, Collins, Liddle, Horwood; Murray (Yantorno 46), Sweeney, Gamble; Brown (McSweeney 77), Monkhouse, Boyd (Hartley 68). Unused substitutes: Rafferty, Behan, Fredriksen, Larkin.
Sheffield Wednesday: Weaver, Buxton, Purse, Beevers, Spurr; Sedgwick, Coke (Miller 76), Potter, Teale (O'Connor 63); Tudgay, Mellor (Morrison 70). Unused substitutes: Heffernan, Jones, Jameson, Ostembor.
Referee: N Swarbrick (Lancashire).
Man of the match: Neil Mellor.