Hill was the man of the match as Sarries claimed a last four berth
Saracens director of rugby Alan Gaffney said his side had proved a point after they stunned the Ospreys to reach their first ever Heineken Cup semi-final.
The Londoners were hammered 30-3 by the Ospreys just two weeks ago but bounced back to win 19-10 on Sunday.
"There's been a lot of things said by the pundits and the press about whether we should have been there or not," Gaffney told BBC Sport.
"Today I think our guys answered the critics, went out there and performed."
World Cup winner Richard Hill was named man of the match after a vintage display from the former England flanker, who has come back from 18 months out with a knee injury.
"People see him limping and he has only got 85% range in that leg," Gaffney said.
"He will never walk without a limp. That's not a problem, it is just the way his leg is. He was phenomenal today and we knew he would be."
Hill, who retires at the end of the season, was overjoyed to have broken new ground as Saracens reached the last four for the first time, where they will face 2006 champions Munster.
"We haven't been in this sort of arena before. We hadn't made the quarters and now we're in the semi-finals - let's savour this win," said the 34-year-old.
"People ask why did you go through what I've been through to come back and play rugby - the time it's taken, some of the heartache, some of the pain. It's for days like today."
Two weeks ago the Ospreys hammered Saracens 30-3 in the EDF Energy Cup semi-finals but Hill, who was man of the match on Sunday, said Sarries were always confident they could gain revenge.
"There's been plenty written and spoken about it in the media - that has been a motivation for us. But there was always belief and we went out and proved it," he said.
"We didn't give them any time to settle on the ball, forced some uncharacteristic mistakes out of some fantastic players and fair play to the pack for that, particularly for the first half.
"Today is all about savouring this win."