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United are reportedly not planning to challenge the sanction, which saw Grimsby hit with a £20,000 fine for their administrative blunder. It is believed the Mariners voluntarily disclosed the breach and the EFL confirmed their verdict, despite earlier FA Cup precedents resulting in teams being ejected from the tournament.
Speaking to BBC Radio Humberside on Thursday ahead of his side's forthcoming encounter with MK Dons, Artell maintained that nothing could diminish a magnificent evening in Grimsby's folklore.
"The club has made a statement and I refer them to the statement," said Artell. "From my point of view as head coach, no one can take away that performance. Nobody can.
"We were the better team for 70 minutes or for 75 minutes. We should have been 3-0 regardless of everything else that has gone off since, and I am extremely proud of the performance of the players, all of the players. I thought we deserved to win the game.
"What happens surrounding that isn't in my domain [to say] but, like I say, nobody can take away the performance of the players and the manner of the victory, certainly not in my eyes anyway. What happened was unfortunate, we owned up, made a statement, let everyone know and we move on."
After their triumph over United, Grimsby suffered a 1-0 defeat to Bristol Rovers last weekend, but they're aiming to bounce back when they take on MK Dons this Saturday. Meanwhile, United almost suffered another loss to Burnley in their following Premier League match at Old Trafford.
United took the lead on two occasions, only for Burnley to hit back twice. However, after Bruno Fernandes scored a penalty in the 97th minute, Amorim's side held on to secure a first win of the new campaign.