Groves' opposite number Gary McAllister stepped up to score from the resulting spot-kick and The Sky Blues went on to take all three points.
"It looked harsh from the sideline and it felt harsh from the pitch," said Groves.
"If it was going to be a penalty and it was deliberate then I would come and hold my hands up. But I was going with him, tried to check and go the other way.
"If I've stood in his way and tried to block him, fair enough, but I just felt I was trying to turn and we collided."
After the penalty, Alan Pouton had dragged the Mariners level again only for City's Jay Bothroyd to pop-up with an 87th minute header to give Coventry victory.