United's U23s Premier League Cup campaign began with a disappointing defeat at Bramall Lane on Friday afternoon.
Ben Folami scored the only goal of the game in the second-half after Jordan Hallam had seen a first-half penalty saved, as Ipswich won the opening Group E encounter.
The first chance of the game went the Blades way in the ninth minute as Parkhouse picked up a loose ball on the edge of the area but his shot flew over.
Less than 60 seconds later, United missed a golden opportunity to go in front. Crowe was adjudged to have fouled Hallam when through on goal, but the goalkeeper saved with his legs at full-stretch from the resulting spot-kick to redeem himself.
The game's decisive goal came just two minutes after the restart, FOLAMI got the better of Graham from Rowe's pass and slotted home to give the visitors the lead. In response, Hallam dragged an effort wide following good work by Smith.
United had the ball in the net on just the hour, but Smith's follow up from Parkhouse's initial effort was ruled offside.
Town almost doubled their advantage as McKendry sent in Folami but Eastwood made a good save with his feet and that was the last action of note as the visitors saw the game out without any further alarms.
Blades: Eastwood, Bennett, Norrington-Davies, Graham (Cantrill 87), Heneghan, Ferguson, Gilmour, Doherty (Graeves 73), Parkhouse, Smith, Hallam (Lawrence 84).
Unused: Hawkes, Warhurst.