Played behind closed doors in Manchester, the fixture was dominated by Gareth Taylor's side. However, a late equaliser earned a 1-1 draw for the visiting Blades.
That makes it one win and one draw from our two friendlies this summer after last week's victory over Durham.
City now have just one more friendly before the Champions League Round One semi-final against Tomiris-Turan in Madrid later this month.
Brighton & Hove Albion are the visitors to the CFA next Thursday, in another match that will be played behind-closed-doors.
Adorned in the new red and black away kit, we enjoyed near total dominance of the ball.
Losada eventually broke the deadlock shortly before the half hour mark with a curling shot from 20 yards that nestled in the bottom corner.
Raso almost forced a second minutes later, closing down a clearance that deflected towards the goal but was retrieved before it reached the line.
Our first chance of the second half came when a ranging cross-field pass from Houghton eventually ended up at the feet of summer signing Mary Fowler, who fired narrowly over from the edge of box.
Raso produced a copy of Fowler's effort moments later, firing a half-volley into the stands.
Sheffield United's first chance came on the cusp of the hour mark but after a melee in the box it was eventually cleared.
A number of changes were made as the match wore on, with several academy players getting an opportunity to impress.
After rounding City's goalkeeper, the visiting striker rolled the ball into the empty net.
But City will have gained a lot from a night on which fitness was more important than the result.
Starting XI: MacIver, Morgan, Houghton, Kennedy, Ramsden, Coombs, Raso, Fowler, Pullen, Losada, Blakstad