"Pat's injury looks serious and it looks like he has dislocated his shoulder," admitted Hill after the game.
"It is a previous injury he has had operated on before and I think he felt something go in his shoulder which was a recurrence of that injury. If it does need operating on that is disappointing because it would mean a six month layoff."
Hill also revealed Goode had been left with a suspected broken nose from the encounter, but the former England fly half would be fit to face London Welsh at Sixways next Saturday.
"In the play-offs now people will be targeting Andy Goode, which is why when we have won the game and got the bonus point, we can bring him off," he said.
"Teams are targeting him, but he has to try and keep his cool even though it is very difficult when people are always having a go at you.
"I do sympathise with him because he is a key player and they do try and get to him. Fortunately today it was quite clear there was a punch and it looks like he has broken his nose, it has made a right mess across his face.
"Andy will be ok though. He seems alright and still has a smile on his face... and we can't have anyone missing a game with a broken nose."