"There was just a little more riding on the match for Quins than there was for Bristol - and that showed through," said Hill.
"Heineken Cup is out the window for us.
"I can now plan for next year by bringing young lads in, rest a few of the old soldiers who have been battling on, let those who need minor operations have them - so basically start planning for next season."
The visitors, drawing 8-8 at the interval, scored tries through wing Charlie Amesbury, full-back Mike Brown, replacement hooker Gary Botha and lock George Robson.
Fly-half Adrian Jarvis kicked a penalty and a conversion - with one goal from replacement fly-half Chris Malone.
Jarvis, joining Bristol next season, was yellow-carded early in the second half - and during his spell in the sin-bin, the hosts were awarded a penalty try to add to the first-half touchdown from wing Tom Arscott - with fly-half Tom Barnes kicking a conversion and a penalty.
Quins director of rugby Dean Richards said: "Full credit to the young boys again - they played very, very well.
"The beauty is that the youngsters are maturing with every game, and they're learning with every game as well."