For 74 minutes Town had led at Sheffield Utd through a Paul Robinson goal on eight minutes - his first competitive goal in three years.
Then United made changes, bringing on towering centre-forward Wayne Allison and Grimsby couldn't cope with the ariel threat.
Groves said: "We didn't deal with the changes that they made. It was one set play, one long punt. We didn't deal with them aerially, we couldn't cope with them when they changed it, it was as simple as that.
"They won every single ball in the air, their flick-ons and direct play just beat us. We had to deal with that way of playing and win the first ball or at least some of them, and we didn't win one."
"Earlier on in the game we opened them up, got down the sides of them and hurt them.
"We scored a good goal and we had opportunities. We looked like we were going to do quite well but as soon as they changed it we didn't cope with it.
"There are a lot of plusses performance-wise, the way the players stuck at the task, the work rate and the general play, but what have we come away with? At the end of the day that is what it is all about. If you don't get the results you don't get the rewards."