Gus had to be euthanised after "tragic medical complications", according to a post Holly and Jimmy shared in late July.
Holly continued in the new video: "We are just so grateful for all the support, we've read all your messages and it's been overwhelming. Thank you."
Jimmy apologised for not being able to respond to all the kind messages but thanked fans for being so kind after their loss.
"We realise that a lot of people have gone through similar things lately and that's really sad," he said, adding that he and Holly are in a "much better place" now.
WATCH: The Bachelor Australia finale: Jimmy chooses Holly in the finale. Story continues.
He concluded: "We're back, ready to get on with our lives and we'll always miss our little Gussy."
The Bachelor couple welcomed Gus to their family in June, sharing regular updates on the adorable kitten on Instagram.
He came into the home after Jimmy and Holly rehomed their Border Collie dog, Billie, sending her to live with Jimmy's parents who have a bigger home.
"It wouldn't be fair to keep Billie in our little apartment. She now gets walked every morning and has plenty of room," he said at the time.
Gus seemed more suited to apartment living for the pair, but just a month later Jimmy and Holly announced he sadly had to be "put to sleep".
At the time, the couple wrote on Instagram: "It is with great sadness that we were forced to make a tough decision to put our little Gus down.
"This is a call we made as a team for the sake of his quality of life following some tragic medical complications.
"No words can describe the heartbreak we are feeling after losing our little man so soon."
This article first appeared on our sister site, Now to Love.
