In an Instagram post Jones said someone would stop him to ask about his dad "every time" he went to see him at University Hospital of Wales in Cardiff.
"He probably taught them at some point," Jones added, referring to his father's profession as a teacher.
Mr Jones was the headteacher of Baden Powell Primary School in Splott, Cardiff.
His son said he was "strict and direct" but "always reasonable" during his 40 years as a teacher and 28 years as a head teacher.
"He made a big impact on education in these parts over a long period of time," he added.
Jones said he was "grateful" to all the NHS staff for the "care and understanding" they showed to his father.
He commended his sister for her ability to care for their dad not just as an NHS worker but as his daughter too.
"She's just been amazing, didn't miss a beat," the post added.
Jones also described his sister's WhatsApp group with some friends, and said it was "so important" to find humour in such situations along with "unconditional support".
"A tough old week. But lucky in so many ways," he added.