"Like everyone, we are doing our best to actively educate ourselves and make more conscious choices to support Australia's indigenous community," he said.
"Before making the purchase, care and research was taken to find an ethical supplier with the sole intention of supporting indigenous businesses and culture.
"It was our understanding the store works directly with indigenous communities to support their craftsman and didgeridoo making families and communities in Arnhem Land.
"In light of feedback yesterday, we have taken time and reflected on how we can do more to educate ourselves to build on our knowledge and understanding of these issues."
The purchase had been described as "problematic" online amid claims the item was bought from a non-Aboriginal business.
"Non-Indigenous people owning or profiting from our culture is very problematic as it reflects a history of carpet-bagging and takes economic opportunities away from our mob," a post on @blakbusiness reads.
Others were quick to label the gift "inappropriate and disrespectful" as well as "shameful", pointing out the Sydney-based influencer had been accused of cultural appropriation in June when she wore her hair in braids for the promotional campaign of her activewear line.
Screenshots taken from Tilse's Instagram stories show he responded to the backlash on Monday, stating there had been "confusion" over the situation.
"I only want to glorify the rich culture that is attached to this country and the land," he wrote. "I am proud to be Australian and want to acknowledge the traditional custodians of the land."
He also shared an article on the yidaki titled "Why the didgeridoo should be our national instrument" that explored its history, explaining it is traditional to clans from Northern Australia but had been embraced and adopted by other Aboriginal people.
Tilse also revealed where the yidaki had been bought, but @blakbusiness claims this store is "not Aboriginal owned".
Sarah, 27, was the centre of a cultural appropriation storm earlier in the year when she wore her hair in two long braids, with colourful strands woven all the way through.
After sharing the images on her Instagram, backlash prompted Sarah to swiftly delete them and eventually reshoot her campaign for Sydney fashion brand White Fox Boutique.
At the time, she said she was "heartbroken" for offending anyone and said she felt she was "walking on eggshells".
"I'm getting full-on hate death threats to me and Fox. It's brutal … I know 99 per cent of you follow me because you love me, but that one per cent – they're crazy," she said.
"I'm not playing the victim, but I'm feeling very fragile."
Instagram page @blakbusiness said they approached Sarah at the time offering education on the topic but never heard back.
Cultural appropriation is the adoption of an element or elements of one culture or identity by members of another culture or identity that has experienced oppression and disadvantage. In Australia, it usually refers to when a non-Indigenous person/organisation/group/business takes an element of Aboriginal or Torres Strait Islander culture and uses it without permission, cultural respect or any form of reciprocity or payment, a post on Community Early Learning Australia's website explains.