"I have the highest regard for the South African Revenue Service. I have seen the minister and I said to him, please forgive me", Magashula was quoted as saying.
"I had an inappropriate conversation with that Mrs [Nosipho] Mba. It was really banter. There was no intention to subvert the recruitment process of Sars.
"You know that I resigned because I care deeply about Sars."
Magashula was speaking to the newspaper from his hospital bed on Saturday where he was being treated for high blood pressure.
On Friday, Finance Minister Pravin Gordhan announced Magashula resigned following an investigation into allegations that he offered a chartered accountant a job at Sars.
"Following the outcome of a fact-finding inquiry into these allegations, Magashula has resigned with effect from 12 July 2013," Gordhan told reporters in Pretoria.
The Sunday Times reported that Magashula said he had not exerted "implicit pressure" by forwarding the CV and said she "competed favourably" with other applicants because she was a charted accountant with six years' experience.
"The banter that I had with this lady is not the level and standard they expect at Sars, and for that I apologise.
"And I apologised personally to the minister and I fell on my sword for that one," he said.
"This is extremely damaging. I honestly thought that I'm doing the honourable thing by walking away... We are accountable and we must do the right thing to protect the reputation of Sars."