Hill insisted that the manner of defeat was unacceptable as the boot of Andy Goode had put Worcester head with less than two minutes to play.
And he challenged his Warriors to now channel that anger and frustration in the right manner as they face up to the challenge of upcoming games with Leicester Tigers and Gloucester Rugby.
Hill said: "I am angry. Everyone is bitterly disappointed but also angry. We have lost that and we have not been beaten by a better team, we have lost it ourselves through ill-discipline which is unacceptable.
"I can see from that performance that we can build on it, there is no doubt about that, but we need to sort the penalty count out. We have got to take our anger out on our next two opponents."
Hill pinpointed a 'crazy' spell after the interval as pivotal as Worcester conceded six penalties in quick succession as Bath rallied from a nine point deficit to level the scores in just 12 minutes.
"We conceded those penalties and that cost us the game," he said. "There has been a lot of chat out there but, as Dean Schofield told the players at the end, it is one thing making noise and it's another not committing penalties.
"Bath played exactly as we felt they would and I thought our game plan was executed very well. We dealt with their kicks, by and large, and were comfortably in the lead at half-time and should have scored a try to put them away.
"Then we had a crazy 12 minute spell after half-time when we conceded six penalties to none and brought Bath out of nothing back to 15-15.
"There was also a lack of composure at end too; all we had to do was claim the restart. There was some over anxiousness over who was going to take it and Andy Goode ends up kicking it when we needed to keep it for a minute and then kick it off the park.
"One of our forwards then infringed at the death. The touch judge gave the call. That has killed us and it's a game we should have won - we have lost it ourselves.
"All you can do is go out and execute your game plan and I was happy with that," he added.
"We played some good running stuff and scored the try, but we have shot ourselves in both feet. The discipline and penalty count will have to be highlighted on Monday morning.
"We knew Luke Pearce would be hot on rolling away from the tackle. We had it written on a whiteboard at half-time to roll away from the tackle, but a few of our forwards flopped on the ball and did not roll away.
"That is not good enough, it has cost us the game and those people will be held accountable.
"They didn't cause us any problems with the ball in hand. But those six penalties at the start of the second half conceded field position. They then kept it until they got the penalties they wanted."