Cordero died at the age of 41 on July 5, leaving behind Kloots and their 1-year-old son Elvis.
"I've talked about everything else about this process and so it feels oddly wrong not to talk and acknowledge about grief," Kloots, who rallied her social media followers to support Cordero during his hospitalization, said Thursday night in an Instagram story, describing grief as "such a weird thing."
Kloots and her family had just moved from New York to Los Angeles at the end of March, when Cordero became sick and went to Cedars-Sinai Hospital with what he thought was pneumonia. The Tony-nominated actor never left the hospital, enduring a months-long stay in the ICU that saw him on a ventilator and suffering from severe complications, including lung infections and a leg amputation.
During that time, Kloots continued to run her fitness business while also caring for their son, finishing the family's cross-country move, rallying support for Cordero and searching for medical cures for his complications.
"I think what's also really hard is that I'm a person that is, I'm a worker and I'm a doer and I'm a creator and I press on," Kloots said on Instagram. "And I don't make excuses for that, but when you're grieving and when you're going through something like this and you go through your day, you feel almost sometimes like, am I allowing myself to grieve? Am I allowing myself to acknowledge what's happened and what's going on and what these last three months of my life has been?"
"I just start to question myself about everything that I'm experiencing right now and how my day to day is so crazy and so busy dealing with so much still and how I'm able to do that but am I also acknowledging everything that has happened and acknowledging my sadness," added Kloots, who said the grief often hits her hardest at night when she is going to sleep. "I don't think there is a right answer to grief or how someone grieves or the process you go ... but it's tough for sure."
Kloots has been writing letters to her and Cordero's son, Elvis, throughout Cordero's illness, and said she also now finds herself talking to Cordero. She said she imagined him getting a kick out of her trying to cope with his death through what she described as her "Type A" and "go, go, go, go, go" personality.
"I was like you know me. This is what I would be doing. I would keep going. I would keep moving. I would keep working. I would keep, you know, doing everything," she said. "And I thought maybe that would make him laugh. Because I think he's listening so I thought, you know me so you know that's going to make you laugh."
Kloots added that she knows the grief is "getting easier every day" but wants to keep talking about it, especially as the number of COVID-19 cases and deaths continue to rise in the U.S.
I just wanted to share because I think that grief is important to talk about, especially in a time right now where a lot of people are suffering from loss from this virus," said Kloots, who ended with a message to her followers about staying safe and following guidelines from health officials.
"I really just want to reiterate though also guys, it's so important to still stay safe," she said. "I know we're all itching to get out and it's summer. I know. I know. But also, just be safe."
"Wear your masks and wash your hands and social distance and just be careful. Just be careful. And get tested if you can. And get antibody tested if you can," Kloots added. "And just be responsible because that's the only way that we will ever end this and that we will ever be able to move forward as a human race."
ABC News' Lesley Messer contributed to this report.