"Unfortunately, we have picked up some injuries. The two positions where we could have done without injuries was in the back row and at loosehead prop," Hill told the Worcester News.
"We were already down two looseheads with Ceri Jones out after a shoulder operation and George Porter having appendicitis.
"Matt will also be out now with a damaged shoulder. We might have to look at if we can bring people in. Oliver Tomaszczyk is also missing with a hamstring injury, so we are light in that department at the moment.
"Neil also looks like he might have broken a forearm. It was a costly match for us in that regard, but it was a brutal game and quite a few of the Bath players went down too."
The Warriors bounced back from an opening Amlin Challenge Cup defeat to Stade Francais to record their first victory in their 2011/12 campaign, away to Banca Monte Crociati in Round 2.
Hill's side face back-to-back games against Bucharest Wolves in Round 3 and 4 with the first game taking place in Romania on Sunday December 11.