Tries from David Strettle and Brad Barritt saw Saracens fightback to secure the victory, but doubts were cast over the second score as Worcester left empty-handed despite what Hill described as a much improved display.
"That was our best performance of the season so far," said Hill. "We were approaching the level of physicality and intensity that we need and I'm disappointed we haven't come away with a point. Our effort deserved it.
"That is the benchmark for us. We need that level of commitment and confrontation to win games, particularly away from home.
"We went to Kingsholm last weekend and did not perform at the level of intensity required. We needed a drastic shift very quickly and we got that today.
"We wanted to win this one and huge effort went in. It was built on solid defence and we couldn't quite make that final pass or movement to score the try.
"My view of the second try wasn't great," he added. "But I have seen it a few times on the TV and it has been concluded that it wasn't a try. We are disappointed about that and you can tell by the reaction of Andy Goode and Alex Crockett that they were annoyed that it was given.
"We have got to move on, but it is a shame because without that we would have got a bonus point out of it, which we deserved today.
"I'm not annoyed. The players are very annoyed, but they were there firsthand. I accept these things happen so it doesn't annoy me, but the players were incensed by it. For them it would have been nice if it had been referred to the TMO."