The Cherry and Whites booked their place in the quarter-finals of the European Challenge Cup thanks to the victory at Kingsholm.
Saints did come back from 21-0 down to go in just seven points behind at the break.
"I think we did some good stuff," Skivington said.
"We've challenged the boys in a different kind of way.
"I was pretty honest last week about where we know we've got to push the game on, and we made a couple of adjustments and the boys looked good.
"We lost control for a little bit, let Saints back into the game but we're building, it's continuous work but there was some real good stuff and some real bad stuff.
"There was some really good bits. There was some good continuity, some boys in the right places.
"Ollie Thorley scored an outstanding try to get the game going so there was lots of positives.
"Just before half-time we lost our way a bit, and Saints are a good side, they scored two tries and all of a sudden the scoreline's not so pretty."