The hosts led 16-11 with less than 15 minutes remaining but three late tries saw their superiority rewarded with a bonus-point victory on a night when Irish's arrival was delayed significantly by traffic.
"It was an absolutely vital game for us to win. The players had a lot of nerves as it was such a massive game for us." Hill said.
Worcester trailed 8-0 at one stage and it was not until 10 minutes from the end that they sealed victory with three late tries.
Hill said: "We made hard work of it. We had a very poor first 20 minutes and we had so many opportunities; we get into their 22 but don't make it count.
"In the end we scored four tries but should have scored at least three more. We have to be more composed but at least we are getting into their own 22 far more than we did last year."
In contrast, Irish coach Brian Smith was a hugely disappointed man.
He said: "We were in control for the first 20 minutes and the game was anyone's at half-time. In the second half we were second rate, it's very disappointing when you haven't performed anywhere near your best.
"We've got to cop it on the chin as we didn't throw any punches in the second half. I'm frustrated that we didn't get into the game at all in the second half."
Irish lost two men, Jamie Gibson & Saliosi Tagicakibau to the sin-bin on which Smith added: "Losing two players didn't help us but the referee was good. Our defence wasn't good enough and we are falling apart at the back end of games which is not acceptable.
"We had this fixture by the scruff of the neck in the first half and I'm very well aware what the issues are."
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