At 1-0 and 2-0 ahead, Grimsby had strikes ruled out, the first for handball and the second following a controversial offside decision. While delighted to have orchestrated a landmark night for the Lincolnshire side, Artell was frustrated that penalties were necessary.
The former Gibraltar international told Sky Sports: "We've had two goals disallowed and missed an absolute sitter to make it 3-0. The disappointing thing, and I'm not trying to be... I don't know what the word is, certainly not live on air!
"We should have won in 90 minutes, that's the kicker for me. It shouldn't have gone to the most ridiculous penalty shootout of my whole career. It shouldn't have taken that to get over the line."
Nevertheless, it didn't diminish what ranks as one of the biggest results in the club's history. Artell continued: "It's a magnificent night for the club and players. I hope it lives long in the memory."
After coming so near to victory in regular time, Artell was questioned about his words to the squad before the spot-kicks. He revealed: "I asked them, what is a penalty shootout? Just one question. A technical challenge, a psychological challenge, that's it.
"No tactics, no physical stuff. You're going to feel nervous, you're going to have butterflies, sweaty palms. That is absolutely normal, it's a human thing, so don't worry about that.
"Then it's a technical thing. Onana's save from the one penalty we missed was an outstanding save. They backed themselves to be good technically, no pressure on them. There was no pressure on them before the game.
"The only thing we could have lost was a bit of pride if we'd got whalloped by an unbelievably good team. Make no bones about it, they've got an unbelievably good team."
Grimsby's prize is a third round tie at crisis-hit Championship side Sheffield Wednesday next month. For the time being, the Mariners' attention shifts back to League Two and their home match against Bristol Rovers on Saturday.