However, with second placed Bedford Blues up next weekend at Sixways, Goode admits Worcester must continue to press on as they chase promotion back to the top-flight.
Goode said: "Things are ticking along nicely for us - the guys are playing really well and there's a great squad. There were a lot of guys back in Worcester who didn't play at Bristol who have been an integral part of the squad this year and that will continue.
"We have to keep working hard - we're 12 points clear now and play Bedford at home on Saturday, which will be a big game.
"Bristol went 20-7 in front in the game and we struggled to get out of our own half," added Goode. "We made quite a few errors defensively in the first 15 minutes and myself and Joey Carlisle had a couple of kicks charged down.
"Eventually, we got ourselves together, though, and knew that if we kept hold of the ball we could do a lot of damage. It was just a case of settling down, cutting out the mistakes and looking after the ball, which we did quite well.
"We knew they'd come out hard and they've started a lot of games well - like they did at Bedford last week. We were a little bit slow and made a few too many errors to start with.
"But we're always confident in our game and the players we've got, so we thought it would only be a matter of time until we settled into our game and really made some inroads.
"As soon as we cut our error-count down, they didn't pose as many threats. We got ourselves back into the game, but then gave away a try off the top of a line-out just through a missed tackle - a simple error that let them into the game. Bristol are a good side and you can't do that.
"The turning point was when we were under our own posts at 20-7 and a few of the senior guys spoke and told everyone that if we cut out our errors, we'd be back in the game."
Goode was also keen to play down his own heroics insisting the victory was down to a team effort and not his fine two-try display and kicking show.
"It was a great team performance and I was lucky enough to get a few points, but a lot of the time it was the forwards and the back-line guys winning penalties, so I was just doing my job," revealed Goode.
"For my first try, Blacky (Adam Black) made a hit, one of their guys lost the ball and I was able to hack it on and win the race - it must have been against their tighthead prop!
"Defensively, it was pretty good - we made quite a few turnovers and I was lucky enough to be on the end of a kick-and-chase."