Forrest said he had already briefed lawyers to seek leave to appeal to the High Court of Australia.
He also said he had plans to set up a new six-team rugby competition in the Indo-Pacific region, with a Perth-based team to participate.
"We're not giving up, even remotely," Forrest said.
"Out of great disappointment there comes great opportunity."
Forrest was speaking after the NSW Supreme Court Justice David Hammerschlag dismissed an appeal by RugbyWA against an arbitrator's decision which backed the ARU's move to drop the Force.
RugbyWA said it expected the ARU would now confirm termination of the Western Force's participation in the Super Rugby competition.
"The ARU had formed the view in February this year that the Western Force were the only team that could legally be removed from the competition," RugbyWA said.
"For the ARU to suggest there was an objective and transparent process, evaluating the merits of both the Western Force and Melbourne Rebels, was misleading and disrespectful to both RugbyWA and the Victorian Rugby Union."
"This has caused significant damage to both the game and the Super Rugby competition and reflects poorly on the ARU's own values of honesty and integrity."
The ARU initially moved to axe the Force from the Super Rugby competition last month after winning an arbitration case against RugbyWA.
RugbyWA argued that the ARU had no power to axe the Force because the governing body signed an "alliance" deal guaranteeing the franchise's future until the end of the broadcast deal in 2020.
But the ARU successfully argued in arbitration that the deal no longer stood because the TV rights have since been renegotiated to accommodate a reduced 15-team competition.