Martha Stewart, who appeared to dress up as a homeless person for Halloween, responded Sunday to a backlash over her costume, saying initially that she had not intended to offend anyone, and then in a second, more contrite statement, adding that she had “really screwed up.” “My earlier statement didn’t go far enough,” Stewart posted on Instagram late Sunday.

“I know many people are suffering economically.

Wearing a costume like I did was insensitive and not funny.

I am very sorry.” On Saturday, Stewart, the 85-year-old entrepreneur, TV personality and media mogul who leveraged her homemaking skills to turn herself into an aspirational lifestyle brand, shared a now-deleted photo of herself on Instagram.

In it, she wore ripped jeans, a torn sweater and a dirtied face.

She held up a clipboard that read, “I Am Hungry Help Me!!” In the caption, she pointed her followers to her branded candle collection on the shopping network QVC, calling them “perfect for Halloween!!!” The criticism that followed was sharp and fairly swift, accusing her of being out of touch, at a time of widening inequality and in an affordability crisis.

“Hunger is not a costume.

It is a reality faced by 47.9 million people (one in seven households) across the country who are struggling to put food on the table,” Crystal FitzSimons, president of the nonprofit Food Research and Action Center, said in a release.

“Stigmatizing images and messaging reinforce harmful misconceptions about who experiences hunger and why.” Some, though, suggested the reaction over a....