Wasps also endured disappointment over the Christmas period with a heavy defeat to Gloucester and sit just three points above Warriors in the Aviva Premiership table.
Hill, though, acknowledges they boast one of the most deadly back lines in the English game and knows his Warriors must produce a more disciplined and resolute performance at Adams Park to return to winning ways.
"The threat from Wasps will come in the three quarters," said Hill. "Leicester had a very good and dominant scrum against us and a very good set piece. We didn't get near their lineout.
"Wasps will be very different, the strength they have is in the backs with the likes of Robinson, Flutey, Wade, Varndell and Haughton. They have an electric three quarter line.
"The problem they had against Gloucester was not getting the ball to them. Our main role will be to stem the flow that they get from the set piece because if their backs get it they are a lot more dangerous than Leicester are.
"It's a quick turnaround and a crucial period that really tests your squad," he added. "We have two teams that have lost the previous game so they have got to get their heads around preparing for what is now a crucial game.
"We are just a few points behind them so a win would jump us above them. But I listened to Dai Young after the Gloucester game and he was talking about a reaction too.
"When you concede six tries to one that is a bit of a thumping while we conceded four tries to one which is not good either. Both teams need a reaction.
"They have probably suffered a bit more than us with injuries, but in fairness to Dai Young he has not used that as an excuse and players have come in to do a job."