"Do I think I deserved to stay in the process given my abysmal selling record? No, not at all," the 24-year-old online fragrance retailer admitted.
Lord Sugar slammed Team Connexus for their poor profits after selling £343.53 of "jumbo" fish cakes and tuna nicoise to City traders and commuters, but having high manufacturing costs of £341.66.
"£1.87 is a disgusting result," he told Connexus, while commending Team Versatile, headed by Selina Waterman-Smith, for their £200.29 profit and treating them to a sushi masterclass from the head chef at restaurant Nobu.
Project manager Jackson, who runs a food blog, was told off for poor team management, while former fish restaurant worker Butler-Smythe was admonished for making only 89 of the team's projected 300 fish cakes, and for making them too large.
But Lord Sugar ultimately fired Callaghan and said: "Part and parcel of the criteria of the winner is they've got to be a bit of a jack of all trades, they've got to be able to dirty their hands, go out and sell, market things and Dan, you've failed on one of the things already in that you can't sell and you say you can't sell."
Callaghan sealed his own fate when he blustered to his fellow candidates "I can't sell, I can't cook - shoot me", but he doesn't regret saying the fateful line.
"It's a very brave man who goes on a programme that's about selling stuff to people and admits from day one that he can't sell anything.
"What I was trying to do was say, 'Well, I am quite good at business, I do have a track record in business, but it's just not in selling or cooking'," he said.
The delivery was reminiscent of The Thick Of It's Chris Addison, who Callaghan admitted he was often compared to.
"Someone wrote in the Gay Times that I was a cross between Chris Addison and Nick Clegg and I didn't quite know how to react to it. To be fair, I don't think that's necessarily the worst comparison. I've worked in politics after all."
Standout moments from Callaghan's time on the show included his team name suggestion of the Sugababes - "That was a great joke, wasn't it?" - and Lord Sugar telling the laid-back candidate to "Take your hands out your pockets".
While Team Connexus were shadowed by aide Baroness Karren Brady, Wednesday's episode was the first time the public had seen Claude Littner take over from Nick Hewer - and he had the candidates quaking in their boots.
"When we first went into the boardroom, there was an empty seat and Lord Sugar said 'here's my new advisor' and Claude walked in. You could hear a pin drop. The atmosphere in the room just changed. It was terrifying, but looking back it was quite funny," Callaghan said.
He said he underestimated how dog-eat-dog the process would be, but that the other team-mates became like family to him, despite his short stay.
"Sometimes you have to put other people down or attack other people and that's something I didn't appreciate as much as I should have when I went in.
"It's an intense process. These people are your colleagues, your competitors, your friends and they're your family, they're the only people you socialise with in the process."
Callaghan confirmed that his family were not disappointed he only made it to the first round, despite previously admitting he had nearly bankrupted them with past business endeavours.
"My family have experienced a lot of difficulties with my business, which they've invested money in. I've spoken to my parents about it, they've been happy for me, and happy I got to take part in such an amazing experience."
After an enjoyable episode of The Apprentice's sister show You're Fired with Jack Dee -where his dressing room was next to Johnny Depp's - Callaghan says he want to pursue media projects.
"My reality TV career is probably at an end, but at the same time there might be other stuff in the media that comes my way."
You're Fired! airs on BBC Two at 10pm, immediately following the main episode.
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