Ms Kapterian on Thursday said she was satisfied the result was correct after a final review of the ballot papers.
Independent MP Nicolette Boele won the Sydney-based seat of Bradfield at the May 3 federal election by just 26 votes.
It was previously a blue ribbon, safe Liberal electorate before she cut the margin down to four per cent at the 2022 election and claimed the razor-thin victory in 2025.
The seat was initially declared for the Liberals before a recount put Ms Boele in front.
Ms Kapterian said ballot paper interpretation was often difficult and subjective.
"In other words, after asking the on-field decision to go to the video umpire, we have had the opportunity to review the play and can now be satisfied the right call was made overall," she said in a statement on Thursday.
"Accordingly we have taken the decision to no longer press the petition for a final review by the Court of Disputed Returns.
"I wish Ms Boele all the best in the role and I thank the people of Bradfield for this incredible opportunity."
Ms Kapterian, who was tentatively named in Opposition Leader Sussan's Ley's extended shadow ministry should she have won the seat, called for a "modern Liberal Party that speaks to the concerns of Australians".
"I am disappointed to miss out on contributing from inside the party room but I will continue to play my part," she said.
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