Rutherford did admit, however, that his 171 from 217 deliveries was a "very special" innings.
"You just do exactly what you do in first-class cricket," Sky Sports News quotes Rutherford as saying. "That was the plan in Queenstown last week.
"It's tougher in this game with Steven Finn and James Anderson bowling. You are out there to do a job and the job is to score runs. The first hundred is very special.
"I wanted to be there for half an hour after the lunch break and then go from there. I don't really like getting out."
New Zealand will resume their innings when day four begins at 9.30pm.