Warriors now entertain Nottingham Rugby in Pool A at Sixways on Saturday (April 2) and Hill is demanding that his team put right any wrongs in that encounter.
"We had overwhelming possession and overwhelming territory so I am very angry that we didn't get the four tries," he said.
"We had enough possession and territory to get six or seven and we have only got three - we will want to put that right next week.
"Our minds now immediately turn to next Saturday and we need to show what we can do and we need to cross the line. So many times we were five metres from the line and coughed the ball up or conceded a penalty.
"I'm disappointed and angry and we will need to set that right next week. I was very happy with the scrum and we had so much possession tonight - there was only one team in it."
Hill also conceded that his team needed to get used to scrappy fixtures in the league play-offs - in particular any potential semi-final in the coming weeks - if they were to secure promotion from the RFU Championship.
He added: "That game was what cup rugby is all about and I have been telling the team that all season.
"We have all enjoyed ourselves playing some beautiful rugby, but when it comes to the semi-final that is what you are going to get.
"In this transition period the team have not really believed me - but come the semi-final it will be about defence, going forward and territory. I think the penny is dropping now.
"The fact we are winning is a bonus, but the team are realising that is a true cup match and that is exactly what we will face in a semi-final.
"It's not about playing pretty rugby, playing wide and throwing the ball around - it is about being direct."