Groves and his players are still under fire following the woeful performance at Wycombe on Saturday. With the Mariners facing high flying Plymouth without the suspended Jason Crowe and Tony Crane, plus injury doubts over Michael Boulding and Stuart Campbell - hopes are far from high.
But Groves has issued a rallying call to his squad, stating that they must prove to the fans they want to win.
"Whoever wears that shirt on Saturday has got to show the fans that it means something to them," he told the Grimsby Telegraph.
"They have to be prepared to fight and scrap for every single ball that there is to fight and scrap for. We'll have to have a cool head, be calm and pass the ball with purpose.
"We'll choose what we feel is the best side on the day. We're looking for the players to show the fans how much it means to them.
"They should be wanting to wear the shirt with a bit of pride. They should want to put on a performance for the fans and hopefully show that it was a one-off.
"I felt we got out-fought from the very off last Saturday. Once that happened it had a knock-on effect and it proved to be disappointing."
The paper has also reported that the players were given today off from training!