Formula One has blocked US outfit Andretti's bid to join the circuit, citing concerns over the team's level of competitiveness.
Andretti, headed up by 1978 world champion Mario and his son, former McLaren driver Michael, had applied to become Formula One's 11th team from 2025 or 2026.
"Our assessment process has established that the presence of an 11th team would not, in and of itself, provide value to the championship," Formula One said in a statement.
"The most significant way in which a new entrant would bring value is by being competitive. We do not believe that the applicant would be a competitive participant," it added.
However, the door was left open for admission from 2028, when Andretti partner General Motors (GM) - which is backing the team through its luxury Cadillac brand - plans to produce its own engine.
The team would have had to use engines from an existing manufacturer until that time, leading to doubts over its ability to properly compete.
"I'm devastated. I won't say anything else because I can't find any other words besides devastated," said Mario Andretti, who raced in F1 from 1968 and 1982 and won 12 grands prix.
Most of the existing teams have been against expansion, put off by the prospect of sharing profits with an additional competitor.
"We would look differently on an application for the entry of a team into the 2028 championship with a GM power unit, either as a GM works team or as a GM customer team designing all allowable components in-house," Formula One said.
"In this case there would be additional factors to consider in respect of the value that the applicant would bring to the championship," it added.
Andretti Global is the parent company to Andretti Autosport and other Andretti ventures, with teams currently competing in seven series worldwide.
They are most prominent in the IndyCar Series, in which the team fields four cars.
Since Michael Andretti's involvement, the team has won the Indianapolis 500 five times (2005, 2007, 2014, 2016, 2017) and the overall championship four times (2004, 2005, 2007, 2012).
"Andretti Cadillac has reviewed the information Formula One... has shared and strongly disagree with its contents," the team said in a statement.
"Andretti and Cadillac are two successful global motorsports organizations committed to placing a genuine American works team in F1, competing alongside the world's best.
"We are proud of the significant progress we have already made on developing a highly competitive car and power unit with an experienced team behind it, and our work continues at pace."
There are currently 10 teams in F1, which is seeking to build on its increased popularity in the United States.
Organisers added a second race in the United States in 2022 in Miami, which joined the race in Austin, Texas, with Las Vegas joining last year.
Audi is scheduled to enter the series in 2026 and Porsche is also in talks with F1, but Andretti must now wait despite receiving clearance from the FIA, motorsport's governing body, last October.
However, the team's place on the grid was subject to it striking a commercial agreement with F1 owners Liberty Media.
"While the Andretti name carries some recognition for F1 fans, our research indicates that F1 would bring value to the Andretti brand rather than the other way around," Formula One said.
"The addition of an 11th team would place an operational burden on race promoters, would subject some of them to significant costs, and would reduce the technical, operational and commercial spaces of the other competitors," it added.
The 2024 F1 calendar is set to feature a record 24 races, starting with the Bahrain Grand Prix on March 2.