Town adapted to the conditions better than their hosts' though and the pace of Michael Boulding, Jason Crowe and Marcel Cas proved too much in the boggy conditions.
Groves was over the moon with the way his team coped with a change in tactics, brought on by the conditions.
"I am delighted with the result," he told the Grimsby Telegraph. "I think it showed some character to come from behind from a decision that we would argue against. We thought it was a bit generous.
"We couldn't really play the football we are capable of, and we changed it a little bit to adapt to the conditions, and credit to the players as they did that.
"It was a day in which you couldn't play in front of teams and pass the ball and try and move it.
Groves also picked out two of his players for special praise. First was Iffy Onuora, who's diving header before the break brought Town back into the game.
"We had to get balls into the box and Iffy can cause problems in there with his aerial presence," Groves noted.
"He did and it was a vital time to get a goal. It got us back in the game and set us up for a decent second half.
"He has been out for nearly a year and that takes some getting over. People are getting used to him and hopefully he can continue playing in the same vein."
Second to get a mention was super-sub Marcel Cas who came on to change the game with two assists for Michael Boulding.
"We had to play percentages with balls in the box, we did that with the first goal and the two goals later on were from pure athleticism," he added.
"If the game opens up and there is grass to run into then Marcel Cas is going to cause you a problem. He is a real athlete, he set Michael up brilliantly and he changed the game.
Groves shrugged off questions regarding Iain Anderson's reaction to being taken off, stating he would hope all his players are disappointed to be subbed. Anderson however may face a spell on the sidelines with sore ribs and a damaged elbow after he was bundled into the advertising barrier early on in the game.