And the west country club have already claimed one notable victim - French champions Stade Francais - whose 17-0 defeat meant Bristol blew Pool Three wide open.
Hill said: "We have to make sure no-one comes here and wins, and this result will send out a statement.
"We really want to make the Memorial Stadium a bit of a fortress."
Harlequins and Cardiff Blues will arrive there on European business either side of Christmas, with Bristol having put themselves firmly in the mix for a quarter-final place.
It was the first time in their 62-game Heineken Cup history that tournament favourites Stade ended scoreless, but they could have few complaints after Bristol fly-half David Hill kicked four penalties and centre Neil Brew scored a late try.
Hill added: "It was probably our best result of the past five years. To beat the French champions is an outstanding achievement.
"We thought we might scrape something like a one-point or three-point win, but 17-0 wasn't anticipated at all.
"We had heard that Stade were worried about our forwards and, when you know someone is worried about you, it gives you a little bit of an edge."