The Warriors head to title play-off contenders Gloucester on Friday night after suffering four successive league defeats. They are without a Premiership win since Christmas and, while being dragged into a relegation battle currently being fought by three clubs - Sale Sharks, London Irish and London Welsh - still appears unlikely, it cannot be ruled out.
Ninth-placed Worcester are currently seven points above bottom club Sale, and Hill said: "We need a couple of wins to get us away from that bottom area of the table, and we will have to work very hard on Friday to try and get the first of them."
He added: "It's a very tough place to go, Kingsholm - a big derby under lights - but we normally perform well in these evening games.
"The players have been in good spirits despite the defeat to Northampton last weekend.
"Gloucester will pose very similar problems to us that Northampton did, and it will be a real challenge to us. Our defence will certainly be tested in the wider areas, as they have got some very sharp players like Jonny May, Charlie Sharples and Rob Cook."
Hill hands number eight Blair Cowan his first Premiership start of the season, while there are also call-ups for Chris Pennell - he replaces injured wing Josh Drauniniu - centre Josh Matavesi and hooker Ed Shervington.
Gloucester show two changes from the side edged out 33-29 by play-off rivals Wasps last weekend, with centre Henry Trinder in for Tim Molenaar and prop Dan Murphy replacing Nick Wood.
"It's very much about keeping the energy in this group of players," Gloucester rugby director Nigel Davies said. "They worked extremely hard last Sunday up at Wasps and were unlucky not to come away with the win. Over the past two weeks, I've been pleased with the performances that have been put in.
"Worcester are fighting hard in the Premiership to ease clear of the bottom three teams, while we are trying to force our way into the top four. There is a lot at stake for both teams."