In her acceptance speech for the Choice TV actress comedy award, Michele said: "I wanted to dedicate this award to Cory for all of you out there who loved and admired Cory as much as I did.
"I promise that with your love we're going to get through this together."
The event at the Gibson Amphitheatre, California, was her first public appearance since the actor's death.
Lea MicheleWhether you knew him personally or just as Finn Hudson, Cory reached out and he became a part of all of our hearts and that's where he'll stay forever so thank you guys so much
Monteith, who co-hosted the Teen Choice Awards in 2010, was found dead in July in a hotel room in Vancouver.
An autopsy revealed the 31-year-old actor died of an overdose of heroin and alcohol.
Michele, who was his girlfriend both on and off-screen, said the show's fans were "most certainly the greatest fans in the world" for their support in the past few weeks.
She added: "He [Cory Monteith] was very special to me and also to the world.
"We were very lucky to witness his incredible talent, his handsome smile and his beautiful, beautiful heart.
"So whether you knew him personally or just as Finn Hudson, Cory reached out and he became a part of all of our hearts and that's where he'll stay forever. So thank you guys so much."
The cast and crew of Glee recently held a private memorial for Monteith.
The show picked up the comedy award at the ceremony while Chord Overstreet, who plays Sam Evans in the show, won the male scene stealer award and Blake Jenner took home the breakout star prize.
One Direction and Selena Gomez were among the other winners at the awards show.
The event was hosted by Glee star Darren Criss and Lucy Hale from Pretty Little Liars.