The European fixture, however, had been right up for grabs in the second half as a try from home scrum half Florin Surugiu saw both teams battle it out for a crucial Amlin Challenge Cup win.
Hill admitted the prospect of having to secure a try bonus point had impacted on the performance.
However, he praised the character of his team as they fronted up in difficult circumstances to battle back from the brink and keep the pool stages alive.
"We knew we had to get four tries and it's always a bit fatal when you know that. You can lose sight of winning the game and just focus on scoring tries," he said.
"We tried to score too soon, we lost our patience a little bit and at half-time the talk was that players had become too individual. Everyone was trying to score the tries by half-time and we were not sticking to the plan that we adopted.
"There was very little attacking structure because, individually, people were trying to win the game themselves. That didn't help us and it made it disjointed.
"I don't think our players can be too happy with the performance," he added. "There were a lot of errors, penalties and turnovers at the breakdown that we have got to sort out.
"But what we did do is show a lot of character to keep battling for that fourth try. We wanted to keep this competition alive to make sure we leave the last game in Paris as a decider.
The Warriors now face a quick turnaround before they welcome Bucharest to Sixways next Saturday (kick-off 3pm).
And Hill has left his troops in no uncertain terms what he expects in the return clash on home soil.
He added: "Bucharest were obviously up for the game and they were lively. Their strength is in the pack and if they get in your 22 they look very dangerous. They certainly weren't soft in defence and unloaded some big hits.
"But at lot of this group had played Monday night at Newcastle and we had done a lot of fitness work. We didn't have time to do as much team work and so we didn't look as well drilled.
"Next week will be different. We will put the team together early and we will be drilling them. I expect a very clinical and organised performance at Sixways."