Bradford loanee Barry Conlon netted twice for the Mariners either side of a superb Nathan Jarman volley as Vale's winless run extended to seven league matches.
Glover said: "We weren't at the races at all and that's disappointing. We've been keeping it tight at the back and injuries led us to play a 4-5-1 formation and that has worked for us away from home but their front-line dominated our defenders too much.
"The only real positive is the latter part of the second half when we came into it but they had the game won by then.
"We gave Grimsby the start they wanted in front of a big crowd and then did the same again in the second half. If we had kept them quiet for 20 minutes then we may have had a chance. But we lost two goals from set-pieces and that is frustrating.
"All we ask is that the players who go out there wear the shirt with pride and passion."