James Hook had threatened to add to Gloucester's woes at home with 22 points for Perpignan but Twelvetrees kept Nigel Davies' side in touch and wing Jonny May sealed a late win with a try.
"Getting 17 points and a win, I'll definitely take that," said Twelvetrees.
"I found out about two o'clock I'd be playing at 10 but we switch things about in training all the time so it wasn't an issue for me.
"It was probably harder for (inside centre) Ryan Mills coming off the bench but I thought he was incredible in his first Heineken Cup start.
"He was a big voice outside me and it really helped. And having a World Cup winner like Mike Tindall alongside you made things very easy for me."
Gloucester had been well beaten by Exeter in their previous outing at home and looked to be heading for back-to-back defeats after Hook inspired the French side to a commanding second-half lead.
But Davies' side forced their way back into the match in the final 10 minutes before snatching the win.
"It's amazing what a week can do for confidence in rugby. Everyone was hugely disappointed after last week's efforts, we let ourselves down and we let the coaches down," added Twelvetreees.
"We wanted to show what we are all about and we are very happy with the result. We were far more composed this week, we are still a young side and we are eager to play good rugby - sometimes too eager.
"We were very critical of ourselves after Exeter but we were a different team this week, we chipped away at the scoreboard and scored some good tries."
Gloucester travel to Munster next weekend and Twelvetrees is wary of an Irish backlash following their shock defeat to Edinburgh on Saturday.
"Munster will be an incredible game, I've never been there so I can't wait to experience the atmosphere over there. We will take the momentum from this win into next week and it's a game we are relishing."