'Gilmore Girls' ' Keiko Agena Wishes She Had 'More of a Friendship' with Alexis Bledel While Filming

Alexis Bledel and Keiko Agena may have played best friends on Gilmore Girls, but they didn't have the same close friendship off-screen that their respective characters, Rory Gilmore and Lane Kim, did on the series.

During an appearance on fellow Gilmore Girls alum Scott Patterson's I Am All In podcast, Agena answered a fan question about whether the two ladies were friends outside of the show.

"I wish we had more of a friendship. That was probably a lot to do with me not making as much of an effort as I should have," Agena, 47, said on Sunday's episode. "But I also think I was so — 'not worried' is the wrong word — but, you know, they work so many hours that their off set time I thought was so precious to them."

Agena continued, "I didn't want to insert myself into that time of their lives. ... Especially with Alexis and Lauren [Graham], I think that they had such a tough schedule."

Asked by Patterson, 62, whether the pair were able to "click right away" while filming the popular drama, Agena had nothing but praise for her former on-screen best friend.

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.

"Alexis is such a wonderful person and I do think that as soon as I met her as a person, you just recognize that she's an intelligent, special individual," the Prodigal Son alum said. "I think that there's part of me that felt protective of her right away as a fellow actor and someone that recognizes how unique of a person that she is."

"So maybe some of that was something that is just instinctual, and I think that probably shows in how our characters related to each other, that we like and respect each other right off the bat," she added.

Last month, Agena reflected on the limitations her Gilmore Girls character had that resulted in Lane becoming more two-dimensional.

"She did everything for everybody else," she said during Entertainment Tonight's A Conversation of Culture: AAPI panel in May. "She was very subservient to her mom, and she became a wife and a mother very early, and she was the best friend. She was the selfless — someone else's best friend. I don't know. That's how I feel about her now. It's not how I felt about her then."

Agena said that she's also "much more protective" of Lane now than she was while filming the series, which ran between 2000 to 2007 and had a four-part Netflix revival in 2016.

"At the time, I was just in survival mode," she recalled. "I wasn't thinking about anything, but now, when I think about her, I sort of wish something better for her."