Worcester gained back-to-back league wins for the first time since April 2009 after they edged past neighbours Gloucester 21-15 at a sold-out Sixways.
It followed a 6-0 success against Wasps last weekend and took them 13 points above bottom club Newcastle with nine rounds of Premiership action remaining.
"We had set ourselves targets in blocks of seven league games," Hill said. "It was 10 points for the first seven and 11 for the next seven, so with one game left in that second block we have exceeded our target by four points.
"I would be mortified if we got relegated now. We felt this game was either going to turn us back to looking over our shoulder, or it was going to mean we could start looking up the table. It was a really pivotal win.
"Last week was our first league away win since April 2009, and now our first back-to-back league wins since then. The players feel good about themselves.
"What this means is that we can genuinely start looking up the table, as opposed to down it. It will give the players a massive boost when they look at the league table."
Former England fly-half Andy Goode guided Worcester to victory after he replaced an out-of-sorts Joe Carlisle at the break, scoring a try, which he also converted, before adding a penalty.
Carlisle had earlier kicked two penalties before Worcester's ex-Gloucester wing Marcel Garvey scored an 80-metre breakaway try.
Hill added: "It was fantastic to see Andy come on and play as we know he can play. He grew in confidence after his try.
"Andy has not been happy, but his attitude has been superb. He doesn't want to be second choice. He has had to sit and watch Joe play well and has had to take his place on the bench.
"But he hasn't moaned. He has been very good in training and he went on today probably determined to prove a point, which is the best possible attitude to have.
"It was made for him, at 10-6 down, to go on and turn the game, and he did so with a fantastic try."
Hill admitted he was "totally relaxed" about his situation at Worcester, despite the club being linked with a possible swoop next season for ex-Harlequins boss Dean Richards.
Richards' three-year worldwide coaching ban, imposed following his role in the Bloodgate scandal at Quins in 2009, expires later this year.
"Dean is a good friend and he would be an excellent asset to any team really," Hill said. "I am totally relaxed about it."
Gloucester were left to reflect on a continuation of poor Premiership away form, having collected a solitary victory from their last 11 league trips.
"In general, I was pretty happy at 10-6 up at half-time, but we started the second half with a missed tackle which gave Worcester momentum," Gloucester head coach Bryan Redpath said.
"I didn't feel we were under a huge amount of pressure from their attack, but our ball-retention wasn't great and that enabled them to create some pressure on us and they capitalised.
"Andy Goode's try was pretty simple - a missed tackle by Freddie (Burns). There was nothing else to it.
"A couple of mistakes cost us dearly today. You have bad days and good days, and today just wasn't good enough in certain parts."
Gloucester's England international full-back Olly Morgan was carried off nursing a knee injury, and Redpath added: "Olly doesn't look great at the moment.
"He is not too comfortable. We will get him scanned over the next couple of days."
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