Welling fell behind early on but battled back with two second-half strikes - meaning they've only lost once at home since August.
Speaking to the club's website this morning, King says his side have to give themselves credit.
He said: "We’ve got to look at it as a very good victory. Chippenham have gone away and beaten Billericay, Torquay, St Albans and Wealdstone. They’re no mugs, they’re a good side.
"Sometimes we have to dig out results and Chippenham are a side who you have to do that against to get any points from them.
"It was a matter of time [before we scored], we were knocking on the door and I felt there was only going to be one winner in the second-half and we thoroughly deserved to win the game.
"It’s another three points at home – our home form is unbelievable.
"I’ve got no complaints, you have to win ugly sometimes and we certainly did that last night."