Elliot Page Credits 'But I'm a Cheerleader' with Helping Him Overcome Early 'Shame' of Queer Identity

Elliot Page is reflecting on some of the media influences that helped him come to terms with his queer identity.

"I, for one, know that without the various representation that I was able to stumble upon as a kid and a teenager — there was very little — I just don't know if I would have made it," the 34-year-old actor said while virtually accepting the Annual Achievement Award at the Outfest Los Angeles LGBTQ Film Festival on Sunday per Variety.

He continued, "I don't know if I would have made it through the moments of isolation and loneliness and shame and self-hatred that was so extreme and powerful and all-encompassing that you could hardly see out of it."

Page then specifically mentioned the 1999 cult-favorite film But I'm a Cheerleader.

"And then, you know, at 15, when you are flipping through the channels and you stumble on But I'm a Cheerleader and the dialogue in that film, and scenes in that film just transform your life," he said. "I almost think we don't talk enough about how important representation is and enough about how many lives it saves and how many futures it allows for."

But I'm a Cheerleader stars Natasha Lyonne as Megan Bloomfield, a high schooler whose parents send her to conversion therapy when they suspect she's gay. While at the program, Lyonne's character falls in love with another teenage girl, played by Clea DuVall.

At Outfest on Sunday, Page noted that the lack of representation for queer people that continues to this day is "infuriating."

"It's [Outfest] and organizations like yourself that are completely changing that," the Oscar nominee said. "And helping get stories out in the world that I know are reaching people in moments where they feel desperately alone and afraid and like they have no sense of community. And it offers somebody a lifeline. And I know that representation has done that for me."

Page came out as transgender on December 1 in an emotional statement posted to his Twitter page. At the time, he said he felt "overwhelming gratitude for the incredible people who have supported me along this journey."

Never miss a story — sign up for PEOPLE's free daily newsletter to stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.

Since then, the Umbrella Academy star has slowly opened up in interviews about his life up until that moment.

In April, he told Vanity Fair he'd always known his true gender saying, "All trans people are so different, and my story's absolutely just my story. But yes, when I was a little kid, absolutely, 100%, I was a boy."