In a game with very few chances for either side, it was the Mariners who took their only real chance of the game during the first half to record victory.
United were unable to capitalise on a string of corners in the first half to restore parity, while both sides came up against strong defences from a number of set-pieces during the second 45 minutes.
Following the full-time whistle, Professional Development Phase Coach Rob Watson believed the game was another one of few chances, with Grimsby taking their one main opportunity on the day to sneak victory.
He said: "Both sides defended well throughout. It was one of those games where there weren’t many chances for either side. They got one and took it. It was disappointing to lose, but on another day, it could have been a different game altogether.
"The quick turnaround from Saturday to Tuesday morning was quite difficult. We only had one day of match preparation before going into what was a difficult game.
"I wasn’t disappointed with the performance, but we maybe could’ve done better with the set-pieces to get some goals. It was a good defensive display from both sides, with two boxes cancelling each other out."
The Iron’s Under-18 side return to action on Saturday morning in the EFL Youth Alliance League when they make the trip to face Hartlepool United (11am kick-off).
IRON: Murtagh, Elliott-Bell, Cunningham, Pike, Strouther, Burden-Whittleton (Abraham, 60), Robertson, Cribb (Dickinson, 80), Moore-Billam (Larkin, 75), Sellars-Fleming, Poulter.
IRON SUB NOT USED: Oxborough.