Law was far from happy with the performance which saw Town drop to third bottom in the table.
"I was extremely disappointed because we didn't compete at all," Law told the Grimsby Telegraph.
"We knew we had players out through injury and had to patch a team together, but that's no excuse for a lack of commitment.
"In the situation we are in, we needed to show real character but there was nowhere near enough out there.
"The players need to take a look at themselves after this, because I can pick a team and show them how I want them to play, but once they cross that white line it's down to them."