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Ebbsfleet boss Steve Brown believes his side should have progressed to the FA Cup first round rather than Dartford.
A 54th-minute Elliot Bradbrook penalty earned the Darts a 1-0 win in Tuesday's fourth qualifying round replay at Princes Park.
Anthony Cook had a penalty saved at the other end, three days after Ben May had missed from the spot in the first meeting at Stonebridge Road. That game ended 1-1.
Brown said: "I’m devastated. Over the course of 180 minutes, the wrong team went through.
"Dartford barely had a shot on target on Tuesday, especially in the second half.
"It’s gut-wrenching for me, for the club and for the players. They’re a league above us and I think that second 45 (from us) was as dominant as you’ll see.
"Whether the goal made them take a step back and protect their goal, I don’t know, but all I know is that’s not the right side going through."
Dartford won the game without five of their key players.
Injury ruled out Kenny Clark, Tyrone Sterling and Jason Prior, while on-loan strikers Matt Godden and Adam Birchall were ineligible.
Manager Tony Burman said: "Steve's entitled to his opinion. I’m absolutely delighted with my players.
"We were on a hiding to nothing when the draw was made, so to have a squad decimated by loan players not being able to play and three of our key players out injured (and still get through) has been a fantastic achievement.
"Ask anybody to take five top players out of their squad and say they wouldn’t be happy with that result.
"We stayed organised and we coped with the pressure. I thought they hurt us more in the first half with their longer balls from the keeper and Ben (May) getting the flick-ons.
"We felt we had to be very careful with the lad (Billy) Bricknell getting in behind and I think we coped with that really well."
Cook is the fourth Fleet player to have missed a penalty this season. He joins May, Bricknell and Michael Thalassitis on the list of those who have failed from the spot.
Brown said: "It’s a pressure-cooker situation. It’s 12 yards and it’s cat-and-mouse with the goalkeeper.
"You have to give the keeper credit, it was a fantastic save and he made a fantastic save late in the game at home on Saturday."
"I’d like to see their penalty incident again. It was soft.
"I think the referee’s been poor and I think the referee at our place was poor. But we’ve also missed two penalties and they’re opportunities.
"How can we do any more? How can I be critical of the players? I honestly believe that if we’d equalised, we’d have gone on to win.
"But we didn’t, so you have to give Dartford credit."
Burman praised his captain's contribution at both ends of the field after Bradbrook left the ground with two cracked ribs.
He said: "Elliot’s put one in with the penalty and then he’s saved the rebound from Alan as well.
"He’s put his body on the line.
"A few of my players did that and I can’t give them enough credit."
Dartford are away to Salisbury in the first round.