They found themselves behind after only five minutes when Salford’s Callum Hendry got the better of Christy Pym from close range to open the scoring.
Clough opted for a back three in defence at the Peninsula Stadium and it often struggled to cope with Salford’s pace in attack.
Brandon Thomas-Asante then made it two for the hosts before the clock had even struck the half-hour mark.
Conor McAleny spotted the space out wide and he played the ball to Thomas-Asante who found himself one-on-one with Pym and smashed past the Stags’ keeper.
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Hiram Boateng had a chance to pull one back soon after when he received the ball after a scramble in the box but the debutant midfielder sliced wide from the edge of the area.
The chances were few and far between for the rest of the first half and Mansfield entered the break two goals down.
But it was an improved performance after it with Jordan Bowery testing Salford keeper Tom King from distance and fizzing an effort just over the bar in the opening minutes.
The Stags managed to get themselves back into the game and began to trouble the hosts in the final third.
Boateng will be left feeling he could’ve done more when he latched onto a cross from Stephen McLaughlin only for his header to bounce off of the ground and over the crossbar.
Rhys Oates had an effort punched away, Lucas Akins failed to connect with an inch-perfect McLaughlin ball, Oates had another saved on the line, but Mansfield failed to dent Salford’s advantage.
Clough’s side will return to league action next Saturday when they host Tranmere in the first home game of the season.
Salford City (3-4-1-2): King; Lowe, Vassell, Nartey; Shephard (Bolton 79’), Watson, Watt, Touray (c); McAleny, Thomas-Asante, Hendry (Leak 87’)
Unused subs: Torrance, Simoes, Smith, Berkoe, Dackers
Stags (3-5-2): Pym; O’Toole (Gordan 80’), Harbottle (Clarke 89’), McLaughlin (c); Akins, Maris (Hewitt 60’), Boateng, Quinn (Gale 89’), Bowery; Swan (Lapslie 60’), Oates
Unused subs: Flinders, Cooper
Referee: Adam Herczeg
Att: 2,721 (1,109 away)