Anderson was shown the red card by referee Phil Prosser after leading with his arm in an aerial challenge with Michael Walsh.
Whilst most the fans were in eventual agreement that Anderson deserved to walk, Groves still defended the Scotsman.
"I believe it was a genuine challenge and he tried to head the ball," Groves said after the game. "I know the lad and he wants to play football, not go out and maim people.
"The referee has deemed it an elbow but I would be surprised if he meant to do that. Players use their arms to get up there."
Anderson joins Marcel Cas and Des Hamilton in the list of shame already this season for the Mariners with all three facing three games suspension. The club have also decided that, like Hamilton's and Cas', Anderson's case will be put forward for an appeal.