The Warriors were undone by an Olly Barkley injury-time penalty against Bath a fortnight ago, losing 24-23, and today it was Gloucester's Freddie Burns who came up trumps to secure a 16-16 draw for his team during the dying seconds.
"A little bit of inaccuracy right at the end has cost us two home wins in the last couple of weeks. It is a bit cruel, and a cruel blow for the players," Worcester head coach Hill said.
"We should have had a couple of scores in the first 30 minutes, yet we just lacked that little bit of composure, but there was a huge amount that was very positive today.
"Our defence was much-improved from last weekend against Leicester, and we've created numerous opportunities inside the opposition 22. Now, we've got to learn to be more composed just to finish those chances off.
"The players are working hard and giving everything they possibly can. For me, there are so many good signs. We will get there.
"The players are absolutely devastated in the dressing room. We've played Bath and Gloucester at home and we should have won both those games."
Andy Goode looked to have secured victory for the Warriors just two minutes before Burns' leveller after Gloucester skipper Jim Hamilton recklessly pushed Worcester lock James Percival at a lineout.
But Worcester could not hold on, and Burns struck with the final kick of an otherwise dire contest to secure a draw when the Warriors infringed at a scrum.
Gloucester centre Henry Trinder and Worcester replacement prop James Currie scored second-half tries, while Goode slotted two penalties and his team-mate Joe Carlisle a penalty and conversion.
Burns, who went on as a second-half substitute, slotted a penalty and conversion from his two kicks at goal and there was a penalty double from Billy Twelvetrees, but neither side covered themselves in glory.
Conditions were ideal for a free-flowing spectacle, yet both teams' repeated failure to master basic handling skills helped render the game largely a non-event.
Hill added: "We haven't got all the points we wanted on the board, but if we keep training as we are doing then we will get better and better as the season goes on.
"I feel bitterly disappointed for the players, but they are a group that is coming together.
"We haven't had the results, but we know if we keep playing as well as we are doing then we will get those results."
Gloucester head coach Nigel Davies has seen his team collect a win, draw and defeat from their first three Aviva Premiership games, and he admitted this encounter had been a poor spectacle.
"It wasn't the greatest game of rugby that has ever been played," he said.
"But from our perspective it was really important we came here and got something out of the game.
"There is a lot more to come from us. I wouldn't like to think we will play that badly again, but we've come here, got two points and it keeps things ticking over.
"A draw was probably a fair result, but I was happy with our resilience and never-say-die attitude and I was also pleased with how we kept our composure in the last play of the game.
"We are finding our feet as a team, with new patterns and new systems, but we under-performed today, we know that."
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