Dianna Agron, who plays the musical show's Quinn Fabray, worked closely with Monteith at the show's beginning, when their characters were McKinkley High's star quarterback and head cheerleader.
"I have never lost a friend. In this difficult time, I am leaning on all of the wonderful memories we shared with Cory, how many ways he was able to make us smile," Agron, 27, said, in a lengthy statement released Thursday. "Glee was a gift to all of us. It gave us a family in this industry. We really cut our teeth and grew up on this show."
"In playing underdogs, we learned that we had dug into the hearts of our viewers and that we could stay there. Cory is so deserving of that place in everyone's hearts."
"He was one of the most generous and kind people that I have ever met. He had a smart, curious mind, he was an enormous talent," she said. "He was loving to not only me, but my family. My heart goes out to his family, to Lea [Michele], to everyone that is struggling with the loss of our friend."
"We will miss you Cory," she said. "We will always carry a piece of you with us."
Agron met for brunch Tuesday with cast mates Jenna Ushkowitz and Jane Lynch, who visited the "Tonight Show with Jay Leno" Wednesday night and shared her own memories of Monteith.
"Cory's one of the biggest hearts, was a real bright light," Lynch said. "He was one of those guys that, he knew he was breathing rarified air."
"The gifts that this wonderful show gave us... He was always aware that it was a gift and he was quite generous," she said.
"He was one of those adventurous types of those people," she said. "I always admired how he would get up...you know, he would fly to Mexico, he'd throw parties for his friends. I don't think he left one day un-lived. He was a real bright light in our family and we've lost a really great guy."
Monteith, 31, died Saturday in Vancouver. An autopsy found he died of a toxic combination of heroin and alcohol.
Ray Liotta sues skin care company over use of likeness
Kim Kardashian, Kanye West reportedly set wedding date