Hill could not hide his disappointment after the game at the manner in which two points had slipped through the fingers.
However, he insisted the Warriors would not let their heads drop and would look to make amends against Northampton Saints next Saturday.
He said: "It was cruel. A little bit of accuracy at the end has cost us two wins over the last three weeks.
"We were on red alert when we got that final penalty because we knew the experience of the Bath game.
"We needed to secure the restart but didn't and then on the scrum it is a case of getting the ball in and away. Gloucester went for it and had nothing to lose, they put an eight man push on it and they had a good scrum and we didn't.
"It is a cruel blow for the players again, to do so much, a lot of it really well, and not win the game.
"The referee pinged us a few times at the scrum. We will have to look at that, whether we engaged too early. It is an area where teams like Gloucester, Leicester and Northampton are very strong.
"It was a tough afternoon for our front five and that crucial one at the end hurt us.
"The players are working hard and are giving everything they possibly can. We just need to be better, more accurate and more disciplined," he added.
"The players are devastated and feel very bad. But we have played Bath and Gloucester here and we should have won both games, we feel we were better on the day and should have won.
"Yes, we haven't got the points on the board we want. But if we keep training like we are doing we will get better as the season goes on. We will pose more problems in attack and finish those chances off.
"We are disappointed but we have created a lot of chances in the 22. A lot of our wok over the next two weeks will be on how to finish those chances off."
Hill also praised the display of Nikki Walker who put 14-months on injury misery behind him to make his debut for the club.
"I think Nikki had a good first game. He has been out for 14 months so we weren't expecting a huge amount from him," he added.
"He will get better and better, he was safe under the high ball, defended well and made a nice break.
"We took him off after 60 minutes and brought on Josh Drauniniu who showed good feet and made some strong line breaks. He looked lively. It's good that Nikki is back and he will go front strength to strength for us."