Dicker launched an application with Rodin to join the F1 grid as a new team, with plans to build and design the car in New Zealand before shipping them to the UK to be operated from the Carlin facilities in Surrey.
Rodin Cars purchased a majority shareholding of the British outfit at the start of the year.
Rodin had pledged to employ a female driver to one of the seats, citing Jamie Chadwick as an option, and was looking at a powertrain deal with Ferrari.
The team was one of four teams to make the second phase of assessment. Rodin was eventually passed over in favour of Andretti's application to join the grid, although Dicker says the FIA's process was "fair" even if he did not agree with the decision.
Andretti's bid will now be assessed by F1 rights holder FOM, amid pressure from the existing teams to keep the number of entries to 20 cars.
Dicker felt that he would leave the door open for Rodin to apply again should the FIA ever open further applications, but felt that his initial bid ticked the boxes for innovation.
"I've been following Formula 1 since the '70s, I wouldn't say that we wouldn't do it [again]," Dicker told Autosport.
"I mean, look, I'm pissed off because I honestly believe that we had a good bid; all the talk about the F1 guys only want to bring in a team if it's going to bring in sort of something new.
"Well, we actually offered something new: female driver, geographic diversity. I can fund it myself personally. None of the other guys who were bidding could do that. They're all bringing in outside money. I mean, I can get outside money as well, but they're only relying on outside money.
"And I thought it was a bit weak, to be honest. Like, we even told them that we'd be prepared to develop our own power unit, because we've got all the infrastructure to do it.
"We only went down the Ferrari route because we figured that was probably a better strategy. But, you know...
"And all this talk about getting a woman into Formula 1, but no one wants to do it. I mean, we were prepared to do it. So, you have to feel there's a lot of rhetoric there, and they didn't really back it up."
Reflecting on the entry process, Dicker explained that he was not entirely surprised that the current F1 teams offered resistance, but felt that their influence amounted to "inmates running the asylum".
Asked in an interview with Autosport if he expected the current F1 teams to be against an 11th member, Dicker replied: "Oh yeah, of course!"
"You know, it's a case of a little club and they don't want to rock the boat. Actually, they don't want anything to change.
"I mean, look, it's crazy that the actual teams would even have any input into the decision to bring in a new team. That's like the inmates are running the asylum.
"The Liberty guys, that's a decision for them, but it really hasn't got anything to do with the teams at all."
