And he revealed he wants the current Worcester squad to target being the most successful in the club's history in the Aviva Premiership.
"This week has been about explaining why it is necessary not to just breathe a sigh of relief because of the distance between us and the bottom but to push on," stated Hill.
"In the six years that Warriors were in the Premiership before, I know the team had difficulties and battled really hard. I have total respect for what they did.
"Every year was a battle against relegation and the moment that relegation wasn't likely there was a big sigh of relief. We need to change that mentality.
"We are playing a team at the weekend that is in a very similar position to ourselves; they are only a few points clear of us.
"But there is no doubt in my mind that the talk of Bath will be pushing on for Heineken Cup. They will not accept that a club of that standing and tradition is relieved to be clear of relegation. They will be talking about winning every game to get Heineken Cup qualification.
"That is the mentality we need - there is no reason why we shouldn't it. We are in the same position as them and have Bath away and then home games against Newcastle and Exeter coming up.
"We have made the players realise that a win down at Bath, followed by two home games, would put us in strong position to move up the table. I think the penny has dropped a little.
"It's all about trying to break the mould and what has happened here year after year, where expectations haven't been so great.
"It is natural, the first time you are in the Premiership, to not look too high. But this is the second period for the club in the top-flight and expectations have got to be raised by supporters and by the players and coaches.
"We would like to be the most successful Warriors squad there has been in the Premiership.I hope the players will be determined to be the best squad this club has ever had."