Whitmore, who has known Flack for around 10 years and replaced her as host on the current series of Love Island, said that "none of this makes sense" after the TV presenter took her own life at the age of 40.
Flack was found dead her east London home on Saturday.
Opening her show on BBC Radio 5 Live on Sunday morning, Whitmore - who on Saturday tweeted her shock that Flack was dead - said she had been "debating whether I should, would or could come on air today".
Her voice cracking, she said: "Yesterday we lost someone before their time.
"We're going to talk about her and give her the respect that she deserves and that she didn't always get."
“Be kind... It’s gone too far... your words affect people.”
Laura Whitmore’s opening link on her 5Live show this morning.
This is incredibly powerful radio about Caroline Flack’s death. pic.twitter.com/ovxZ1NDeKh— Steve Holden (@SteveH1982)February 16, 2020
Whitmore, 34, said that "anyone who knew Caroline knew she was vivacious, loving, and had a passion for life, which is why none of this makes sense".
"Caroline loved dancing. Angels by Robbie Williams always reminds me of her because she danced so beautifully to it on Strictly, and I'm going to play that song after I've said what I want to say."
She said that Flack "loved music, she loved to dance, we shared many a dancefloor at gigs, festivals" as she recalled their friendship beginning 10 years ago at V Festival.
"She was bubbly, and for such a small stature commanded a room," Whitmore said. "She loved to laugh and had the most infectious chuckle.
"She also had many struggles. I'm not going to pretend she's perfect, but she lived every mistake publicly under the scrutiny of the media."
Whitmore said that Flack "loved to love" and "that's all she wanted, which is why a show like Love Island was important to her because the show is about finding love, friendship, having a laugh."
Defending the ITV2 programme, she said: "The problem wasn't the show, the show to work on is loving and caring and safe and protected. The problem is, the outside world is not."
She said that people who are ever nasty to others on social media "need to look at themselves", and added: "To the newspapers who create click-bait, who demonise and tear down success. We've had enough.”
"Be kind, only you are responsible for how you treat others and what you put out in the world," she said. "I want to use my platform to call people out because it's gone too far."
She added: "I'm going to carry on today and get through this show as that's what Caroline would say to do.
"Caroline, I'm so sad for you, for your family. I'm angry that you saw this as your only option as I know how much love and support you had. I'm sorry you didn't know that."
"I'm not sure when but I know I'll see you on the dancefloor again."