The Somerset ace, along with captain Alastair Cook, have batted the tourists into a position where they can rescue a draw from the first Test match in Dunedin.
The skipper was removed late in the day for 116, but Compton will resume day five on 102 not out alongside Steven Finn (0).
"It's hard to put in words," the 29-year-old told Sky Sports News.
"I'm just delighted, I never thought I'd be standing here with 100 to my name. You have to pinch yourself.
"I was just trying to keep composed. Part of me wanted to just get on with it during the new ball. It was good that I could keep calm."
England are on 234-1 in their second innings.