Speaking on her BBC Radio 5 Live show on Sunday morning (16 February), Whitmore called out “clickbait” news and online trolls for their treatment of Flack.
A lawyer for the Flack family confirmed that Caroline took her own life and was found in her east London home.
Flack was set to face trial in March over allegations that she had assaulted her boyfriend Lewis Burton at her flat, which she denied.
She stepped down from her role as Love Island presenter following the allegations and was replaced by Whitmore for the winter series.
Opening her show, Whitmore said she had been "debating whether I should, would or could come on air today".
"Yesterday we lost someone before their time,” she said.
"We're going to talk about her and give her the respect that she deserves and that she didn't always get."
Whitmore said "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,” she continued. “'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 making friends with the presenter 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 Love Island, Whitmore 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 cruel to others on social media "need to look at themselves", and added: "To the newspapers who create clickbait, who demonise and tear down success. We've had enough.
"I've seen journalists and Twitter warriors talk about this tragedy and they themselves have twisted what the truth is. You don't have to tear someone down to feel good about yourself.
"So to listeners, be kind, only you are responsible for how you treat others and what you put out in the world."
The tabloid press has come under fire for its treatment of Flack in recent weeks and, following her death, The Sun rushed to remove an article about a Valentine’s Day card which poked fun at the presenter.
Whitmore said she herself has "been harassed for just doing my job and this is where the problem is, and I want to use my platform to call people out because it's gone too far”.
"Your words affect people. To paparazzi and tabloids looking for a cheap sell, to trolls hiding behind a keyboard, enough."
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. But I hope you are at peace and know that you are loved."
Whitmore had previously shared a picture of herself and Flack on Instagram, saying she was “trying to find the words but I can’t”.
If you or someone you know is struggling with mental health, you can reach out for confidential support at Samaritans by calling 116 124 or visiting their website.