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.
Source: Autosport