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."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
$29.99
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.
