The Warriors recorded a 29-23 triumph at Sixways Stadium to give them a first league win of the year.
"There was a lack of crucial errors at crucial times by individuals tonight," Hill told Sky Sports News.
"It was about time all parts of our game came together and there was a real excitement in the team. The intent was there to try to score tries.
"We have got a very fit squad at the moment. No one is tired. We have looked after the players, and this is the time to come good."
The win has moved ninth-placed Worcester 13 points clear of the relegation zone.