The decision not to contest a stewards' decision to strip Hirvonen of his first win for the team in Portugal last weekend meant Norwegian Ford driver Mads Ostberg could finally celebrate his maiden victory in the world championship.
"Citroen Racing had initially stated its intention to appeal against the decision of the stewards," the manufacturer said in a statement.
"Further analysis of the matter did not uncover any new technical elements. After consulting with various experts, Citroen Racing has therefore decided against pursuing the appeal with the FIA's International Court of Appeal."
Hirvonen finished first in Portugal on Sunday, with the 25 points sending him nine points clear of Frenchman Loeb, who had crashed out on the first day, after four rallies.
However the Finn was then excluded from the classification after his car failed post-event scrutineering and Ostberg was promoted to first. Russian Evgeny Novikov finished second with Norway's Petter Solberg third in a Ford 1-2-3.
The exclusion meant Loeb stayed top, four points clear of Solberg.
Champions Citroen had said they would appeal, leaving the results provisional, with a further 48 hours allowed for them to confirm a move that would likely have been both long and costly.
"We had stated our intention to appeal in order to give us time to analyse the matter in more detail," said team principal Yves Matton.
"As regards the clutch, our supplier has sent us a letter of apology acknowledging the existence of a batch of parts which were different from those on the homologation documentation. This letter confirms it was never our intention to cheat.
"At the same time, this situation forces us to look again at our procedures, since these parts were not picked up during our own checks."
Hirvonen, who raced for Ford last year, said he was disappointed but not angry.
"These things happen. You have to accept them when they do, learn the necessary lessons and go again. Citroen has done a lot for me in the last few months so I stand united with the team at this difficult time," he said.