Fighting back tears on her BBC Radio 5 Live show, she said the former Love Island host "loved to love".
She also appealed to listeners to "be kind" to others and said she wanted to use her platform to "call people out".
"To paparazzi and tabloids looking for a cheap sell, to trolls hiding behind a keyboard - enough," she said.
A lawyer for Flack's family said on Saturday that she had taken her own life.
The 40-year-old had been "under huge pressure" since she was accused of assaulting her boyfriend Lewis Burton in December, her management company said.
Burton, who did not support the ongoing case against Flack, wrote an emotional tribute to the presenter on Instagram on Sunday, promising the star he would "be your voice baby", and that he would "try [to] make you proud everyday".
"I am so lost for words I am in so much pain I miss you so much I know you felt safe with me you always said I don't think about anything else when I am with you and I was not allowed to be there this time I kept asking and asking," the 27-year-old tennis player wrote.
He concluded: "I love you with all my heart."
Bail conditions had stopped Flack having any contact with Burton ahead of her trial next month.
ITV cancelled the scheduled broadcasts of Love Island on Saturday and Sunday but said that the show would return on Monday night with a tribute to its former presenter "who will be forever in our hearts".
Whitmore, who took over presenting Love Island following Flack's arrest, said her friend "loved to laugh" and had the "most infectious chuckle".
"I'm not going to pretend she was perfect, but is anyone? She lived every mistake publicly, under the scrutiny of the media.
"Caroline loved to love. 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. The problem wasn't the show. The show... is loving and caring and safe and protected.
"The problem is, the outside world is not. Anyone who has ever compared one woman against another on Twitter, knocked someone because of their appearance, invaded someone else's privacy, who have made mean, unnecessary comments on an online forum - they need to look at themselves," she said.
Whitmore said she had been debating whether she "should, would or could come on air today" but she wanted to talk about her friend "to give her the respect she deserves".
She said she had also been harassed for "just doing her job" and "words affect people".
"So to listeners - be kind. Only you are responsible for how you treat others and what you put out in the world," she said.
She then played Angels by Robbie Williams, saying her friend, who she met at V-festival about 10 years ago, loved music and loved to dance, and the song always reminded her of Flack because she "danced so beautifully to it on Strictly".
"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," she said just before she played the song.
"I am not sure when, but I know I'll see you on the dance floor again and I hope you are at peace and know that you are loved."
Flack had co-hosted The X Factor and won Strictly Come Dancing in 2014, as well as presenting ITV's Love Island.
Following her death, an ITV spokeswoman said she was a "much-loved member of the Love Island team". The show did not air on Saturday night.
The presenter stood down from the dating show after she was charged with assault in December. She denied the charges.
You’ll never be old and wise if you weren’t young and crazy.