Paul Mullin gave Wrexham the lead as he successfully challenged the guests’ central defenders, then slotted the ball into the bottom corner, giving the keeper no chance.
Wrexham’s Phil Parkinson was shown a yellow card for standing over the ball and blocking an opponent’s quick free kick after 80 minutes.
Luke Waterfall’s winner in the 119th minute sealed a 5-4 victory for Grimsby in a vibrant semi-final at the racecourse.
Parkinson’s was not satisfied with a series of decisions made by Adam Herczeg.
“How the league put the referee in charge of this game is absolutely beyond me. I’m absolutely boiling,” Parkinson said.
“His performance was well below the accepted level for a match of this magnitude, it was incredible.
“Congratulations to Grimsby, they have arrived and good luck in the final.
“There was a lot at stake. There are two fantastic football clubs, owners who have invested money in the clubs, and have put a low level referee in a match of this magnitude.
“We had this referee two weeks ago and the way they put him in charge of this match I’m blown away.
“We scored a goal that he couldn’t stand, we had a player who was fouled before his goal and we did [Bryce] Hosannah hit that from around 35 yards out and Hosannah and couldn’t do anything about, dipping and swerving, it did him all ends up.
“I don’t seem to have returned any of these incidents, but dear, that performance was bad.”
Herczeg had officiated the last Wrexham regular season game against Dagenham & Redbridge.
Wrexham had finished runner-up in Stockport County, losing the title and automatic promotion.
Against Grimsby, Paul Mullin’s penalty gave Wrexham the lead, but John McAtee equalized with Waterfall putting the visitors ahead.
Ben Tozer and Mullin made it 3-2, and although Ryan Taylor and Mani Dieseruvwe restored Grimsby’s lead, Jordan Davies equalized to send the tie into extra time before Waterfall’s final winner.
Parkinson said the defeat was “as tough as possible,” with Wrexham now facing a 15th season out of the EFL.
“We are 30 seconds from the penalty spot and concede a goal of this nature,” Parkinson added.
“If they’re pens they’re pens, we know it’s a 50/50 situation, so it hurts.”