Saracens' hopes of finishing top of the Premiership were dealt a huge blow when Worcester pulled off the shock win.
Saracens took an early 8-0 lead and for most of the first half the Warriors struggled to contain the visitors who played a game of huge tempo.
The home defence looked sure to crack and a heavy defeat for the Warriors seemed probable but somehow Worcester held on, grew in confidence, and ultimately secured an unlikely victory.
A delighted Hill said: "The Saracens were scintillating in that first half hour. I was sitting on the bench thinking to myself, this is going to be a long night.
"We were just hanging on in there and they should have scored a couple of tries."
A penalty from Andy Goode and a converted try from Alex Grove just before the interval saw Worcester enjoy a scarcely believable 10-8 half-time lead.
Hill added: "That (Grove's) try was massive as it gave us the impetus we needed just before half-time.
"We knew they could run out of steam as they had a much quicker turnaround than we did (Worcester played last Friday at Sale whilst Saracens faced Leicester last Sunday).
"In the second half they kicked the ball a lot more and played into our hands."
Hill accepted his side had vastly improved.
"Our attitude is now much better. Earlier in the season we didn't have a tough enough mental attitude as we gave away home games against Wasps and Harlequins but that's not the case now.
"This win was massive as we can now stop looking over our shoulder at what's below us in the table and we can concentrate on moving up."
Disappointed Saracens coach Mark McCall rued his team's performance, saying: "We played brilliantly for 30 minutes but we missed a couple of opportunities. After that initial half-hour we lost the penalty count 12-1, which is incredible.
"We are unbelievably disappointed but we have to be more disciplined and more composed."
Saracens have now lost their last two games and face a difficult match against Northampton next Sunday. McCall accepted this would be a tough game but said: "We have six games in the regular season to play.
"We want to get into the top two so as to ensure that we have a home semi-final."
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