But Hill insisted his players still had lots of work ahead of them as they prepare for a trip to Plymouth Albion next weekend.
"I would rate the team four out of ten for that - and they didn't disagree when I told them that in the huddle," said Hill.
"They admitted that there is work to do, but it is the first time that they have played together as that 15 and I would hope that is a good start and we will get better.
"There were some good patches from us, but enough for a coach to go away and know we have still got a bit of work to do. At half-time we should have had two or maybe three more tries, we have got to be more clinical.
"We have got to work on our defence, that might seem silly as we kept a clean sheet, but that was some last ditch tackling.
"Our first up tackling should have been firmer, we allowed Birmingham to make some line breaks and get around us. It was some desperate defence right on our line to keep them out.
"I'm pleased that we kept them out because that was one of the objectives, but they still made a bit too much ground.
"Against teams like Birmingham we have also got to keep the ball for six, seven or eight phases. In the Premiership you can keep the ball for 15 phases and the defence is still rock solid.
"In the Championship, in my experience, if you keep the ball for two or three phases the defence is organised. But if you can keep the ball for six, seven or eight phases that is when they become disjointed.
"In the second half I was disappointed that we made a few silly errors and lost the ball after two or three phases. Then it was another scrum, it just slowed the whole thing down.
"To really put these sides under pressure we have got to string the phases together, even if they go down injured or with cramp the ball is still in play."
During the game Worcester lost both Neil Best and Jake Abbott to the sin bin and Hill had contrasting views of both yellow cards.
He said: "The second one to Neil Best I will justify because they were probably going to score a try. Call it a professional foul, but the side knew after my talk at half-time that Birmingham were not to score a try.
"They had a golden opportunity to do that and Neil took one for the team and slowed that ball down. It was illegal and quite rightly got a yellow card, but it did stop us from conceding a try so I guess it was the lesser of two evils.
"He either gets a yellow card or the side has to face me at the end of the game having conceded a try. I think he felt the best option was to sacrifice himself and take a few minutes in the sin bin.
"The first sin bin Jake will learn from. He is being pulled and he reacted. You can't take justice into your own hands. He is a young lad who will learn, he apologised when he came off, but other than that he had a great game."
Warriors were backed throughout the afternoon by a vocal crowd of 6,543 as the sun shone on Sixways.
And after the game Hill was quick to praise the atmosphere generated inside the stadium by a passionate home support.
"I thought the crowd was tremendous," he added. "The feeling around the ground is that they enjoyed their afternoon. Players and supporters enjoy winning and they saw some tries today.
"I would hope that every week the crowd will get bigger and bigger, but the ones who came in today were terrific and created a great atmosphere."