Goode, a former Leicester and England No 10, was shown a red card in the 35th minute for a clumsy high tackle on England flanker Tom Croft and could be cited and banned if hauled before a Rugby Union disciplinary committee.
Goode had already been sin-binned and, while Hill said Goode was sent off for a second yellow card, the officials said it was for a straight red.
Hill said Goode could not be blamed for the seven try defeat by Leicester who moved into second place ahead of champions Saracens, who play leaders Harlequins on Saturday.
Hill said: "He has let the players down to an extent but you can't blame anyone, it was one of those things.
"Andy wouldn't have wished to do that at his previous ground. Andy is distraught, he is really disappointed about it and he has apologised to the players.
"It was pretty tough after that. Once down to 14 men we had to reshuffle and at half-time we put a 10 on and we were down to seven forwards.
"It was hard all night. Leicester were exceptionally good in patches and I think we did as well as we could."
Hill said he was not worried about being dragged back into a relegation dogfight after Newcastle's win at home to Sale.
He said: "That's not a worry to me. I don't think many people would have had us down to win at Welford Road. We just wanted to give a good account of ourselves.
"Most people would have had Newcastle down to win at home to Sale. "Although we are not mathematically secure yet but we have got two home games and we are unbeaten at Sixways.
"We will regroup and make sure we are at full throttle against Exeter."
Leicester director of rugby Richard Cockerill felt Goode's challenge on Croft was rash and not malicious adding: "I know Andy very well, he played here for a long time.
"I'm sure it's not the way he would have liked to come back and have that happen so it's disappointing for him.
"Hopefully the red card will be sufficient and he can play the rest of the season."
Leicester scored seven tries through Scott Hamilton, George Chuter, Croft, Martin Castrogiovanni, Thomas Waldrom, Tom Youngs and George Ford as they continued their quest for a top-two spot and a home semi final.
Worcester scored a late try through replacement Ceri Jones.
Cockerill was not totally happy with Leicester's performance. "It was disjointed and hard to play against a side that did not come to play," he said.
"We were inaccurate for large parts of the game which was frustrating but job done, it's five points.
"We don't want to use up our best performances in games like these, we want to save them for the big ones."
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