Grimsby was fined for the transgression, but remain in the competition as a defeatist United chose not to appeal the result. The FA have thrown teams out of their competition for similar lapses.
"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 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."
The appearance of Clarke Oduor, on-loan from Barnsley, was at the heart of the issue. Oduor's registration had been made past the recognised deadline, so making him officially ineligible for the tie.