Ian Paisley Jnr says his family's political "brand" has not been damaged by his resignation.
Ian Paisley Jnr will continue as an MLA for North Antrim
Speaking at one of his last functions as junior minister, the DUP assembly member said he was delighted at the support shown by members of the public.
"At the end of the day, I've never lost touch with the grassroots," he said.
"If I was a dosser, a time-waster, if I was someone who just used the position for position's sake, I couldn't show my face to people."
He added: "I have been overwhelmed by the amount of calls, letters and the reaction I get when I go into public."
Mr Paisley was speaking to the media for the first time since Monday's resignation, at an event to promote the North West 200 motorcycle race.
He was just back from Edinburgh, where he had been part of a Stormont delegation meeting Scottish counterparts.
On that visit, his first minister father had refused to answer questions about his political future sparked by the resignation.
But Ian Paisley Jnr said his father had always been under political pressure throughout his career.
"As he said, he has a 'rhinoceros hide' and he does it in his own characteristic way," he said.
"The Paisley brand, in terms of governing Northern Ireland, has been very effective, not only in Northern Ireland but across the United Kingdom and across the world."
He said the response he had received from well-wishers since his resignation showed that the brand had not been damaged.
"A lot of people are perplexed as to why it had to happen," he said.