Cory was remembered as "a beautiful soul" in a moving segment at the awards ceremony, which was held at the Nokia Theatre in Los Angeles.
Cory, who played loveable high school quarterback Finn Hudson, was found dead in Vancouver, Canada, in a hotel room on 13 July 2013. An autopsy later ruled the 31-year-old's death was due to an overdose of heroin and alcohol.
Speaking on behalf of the cast and crew, Jane began: "This summer on our show Glee we suffered a painful death in our family. From the first time you saw Cory, he had a star quality and genuine sweetness that made it impossible not to fall in love with him.
"And millions did fall in love with Cory and I'm here to say that all that warmth and that charm and that open-hearted quality that we loved in Cory was no act."
The actress, who plays tough-talking cheerleading coach Sue Sylvester, told Glee fans that Cory was "not perfect" but was still "worthy of your love".
She continued: "Cory was a beautiful soul. He was not perfect, which many of us here tonight can relate to. His death is a tragic reminder of the rapacious, senseless destruction that is brought on by addiction.
"Tonight we remember Cory for all he was and mourn the loss of all he could have been. To a generation that loved Cory so, please know this gifted and wonderful young man was worthy of your love."
Jane added: "And if you were lucky enough to know Cory as we did, and witness firsthand Cory's goofy, breezy sense of, his natural instinct for inclusiveness and his unbridled sense of generosity day in and day out, I promise you'd have loved him even more."
Cory was one of five late stars selected for a special tribute at the star-studded ceremony. Also remembered was Sopranos star James Gandolfini.
It was recently announced that Glee would write out Cory's character in an episode that tackles the actor's real life struggle with drug use.
Watch Glee's official memorial card for Cory here: