Warriors now return to home soil to face a dangerous London Welsh side who also gained a bonus point victory over Nottingham and Goode believes Worcester must go up another gear as they look to navigate the play-off system.
"We knew Bristol would bring physicality, we talked before the game about it being one of the most physical games we would face," he said.
"They chucked everything they had at us and we defended very well. We didn't play as well as we would like, but came away with five points. For an average performance that is not a bad start and we coped with the physicality.
"There is much more to come and to win 44-15 and not play that well can only be a positive, we have got to be more accurate. In attack we made some errors, we didn't always kick well and we went in at half-time leading 20-3 not having played well.
"But our defence was outstanding and when we looked after the ball we looked dangerous and to score tries."
Goode had another busy afternoon as tempers flared at times, but insisted the confrontational battle came as no surprise to him.
"Most sides will get into the ten and try and disrupt the attacking game, that is part and parcel of being a ten and I have got to live with it," he added.
"I am going to get targeted as is Neil Best and Kai Horstmann in the forwards. Across the field we have got a quality squad and we are there to be shot down. It's a cup final every week."
Watch Andy Goode and the Warriors in action this Saturday at Sixways. Call the Warriors Box Office on 01905 454183 or click HERE to buy your tickets online.