Kiwi fly half Nick Evans secured the points for Quins with a late drop goal, but a losing bonus point was the least Worcester deserved for a display at Twickenham Stoop again packed full of intent and passion.
"I was very pleased with the performance and the effort that went in," said Hill.
"We've been able to have that passion, intensity and desire at home under lights at Sixways with the crowd behind us.
"After last week against Saracens, it was about trying to replicate that away from home, which is not easy, and today the players gave everything.
"I wouldn't say that the quality was there at all times, but in the past we have come away from home and not had that desire. We haven't been able to generate it when we've not had a crowd behind us.
"That was a big step away from home, to have a real belief that we could win. To come here and outscore them by two tries to one was a psychologically a big boost for us.
"We had to play 20 minutes with 14 men and the penalty count was 20 to 10 against us. When you are facing that, to still score two tries to one and lose by three points was a good effort."
Hill also praised the manner in which his Warriors frustrated Quins for long period in ice cold conditions.
However, he admitted a lack of parity in the set piece and high penalty count - that saw two players yellow carded - had ultimately cost his team more.
Hill said: "It was stop-start but that is what you have to do to Quins. They like a fast and frenetic game; you can't afford to play a helter-skelter game against them.
"You have to make sure you dictate the pace of the game yourself and at times I thought we were quite intelligent.
"We looked at their front five and our front five and felt we should have the edge, with the age and experience we had in the pack. That didn't happen and if our scrum had got parity we would have won the game," he added.
"Every time there was a scrum we conceded ground through a penalty and they were able to kick to touch and relieve any pressure.
"The players are disappointed and we will have to get on it and work on it because we are better than that.
"We were a bit dull in our penalties. The referee was going to be hot on the breakdown and we were not rolling away.
"We were keeping hands in after the tackle and after two or three seconds, if the referee hasn't given you a holding penalty, then you have to let go because it is a ruck.
"We didn't really listen, we were perhaps too keen to turn ball over and slow them down because you can't afford to let them have quick ball. In our aim to do that we conceded too many penalties.
"The penalties and the breakdown were the two areas where it was disappointing."