Coady has joined the Blades on a six-month loan deal from Liverpool.
McDonald was left out of the side on Saturday as he considered a move after Wolves triggered a clause in his contract.
Coady, who had impressed against Burton Albion in midweek, came in and acquitted himself well after being handed the opportunity by Liverpool chief Brendan Rodgers to gain more first-team experience with the Blades.
The 20-year-old, who captained England at the recent Under-20 World Cup in Turkey, became David Weir’s sixth signing since he became manager of the club in June.
But there was little Coady, who received a booking during the encounter, could do to affect Saturday’s result against a Brentford side who also lost in last season’s play-offs.
Will Grigg scored twice on his home debut as Brentford claimed their first win of the season.
Adam Forshaw opened the scoring when he curled the ball past Blades goalkeeper George Long, who is in the England Under-21 squad for tomorrow night’s match against Scotland at Bramall Lane.
United dragged themselves back on level terms in the 56th minute.
Bidwell’s stop prevented Coady from tapping home Williams’s low cross but, from Murphy’s resulting corner, central defender Neil Collins escaped his marker to head emphatically home.
Six minutes later, however, Brentford regained the lead.
Forshaw robbed McGinn of possession near the by-line before dragging the ball across the area for Grigg to slide home.
Grigg claimed his second, in the 75th minute, after Long could only parry Forshaw’s cross.
The United goalkeeper denied Grigg a hat-trick when, four minutes later, he saved his penalty after central defender Harry Maguire had been harshly adjudged to have brought him down.
Blades manager Weir said: “Obviously we’re very disappointed – I don’t think you’ll win a game losing three goals. It’s very difficult to lose three goals, and try and win the game.
“I was disappointed by the way we conceded the goals and disappointed with certain aspects of it especially after getting back into the game.
“I thought we were a little bit sloppy in regards to decision-making at times and at crucial moments in the game, and that ultimately cost us.”
Weir will be looking for an improved performance when the Blades entertain Colchester on Saturday.
Brentford: Button, Logan, Craig, Dean, Bidwell, Forshaw, Saville, McCormack (Reeves 77), McAleny (Fillo 68), Donaldson, Grigg (El Alagui 85). Unused substitutes: O’Connor, Saunders, Bonham, Javi Venta.
Sheffield United: Long, Westlake, Collins, Maguire, Williams, Murphy (Porter 74), Doyle, Coady, McGinn (McFadzean 74), Brandy, Taylor. Unused substitutes: Howard, Hill, Flynn, McGinty, Whitehouse.
Referee: Andy Woolmer (Northamptonshire).