Hill admitted his team was 'bitter' after the manner of defeat and apologised to supporters for the defeat.
And he urged his players to pick themselves up and focus on the visit of London Irish next Saturday to make amends.
"We are disappointed to lose the home record - it was a real objective for us," he said.
"We have got to make sure we respond. You have to turn those disappointments into positives, let it make you angry and make you work harder.
"We are all very bitter at the moment. But you have got to take that and accept the defeat sometimes and swallow it.
"It is not pleasant, but we have got to make sure we take it out on London Irish next weekend and make up for the fact we have lost this one in front of our fans.
"They (our fans) have been absolutely brilliant and I am very sorry to all the supporters for losing that home record.
"Exeter are a good team and at the moment just a little bit better than we are, that is the standard we need to be reaching next season."
Hill was also left to reflect on the fact his team now remain nine points of bottom spot - and not yet mathematically safe - with two games left to play.
"Yes, it is still mathematically possible to be caught, we would have liked to put that to bed today," he said.
"With Saracens playing Newcastle next Friday night we should know before we play London Irish what we need to do.
"It is still difficult for Newcastle to catch us, in terms of them getting two bonus point wins to overhaul us. That will be tough against Saracens at home and Wasps away. But they could do that.
"That means next Saturday we need to look after ourselves. It is in our hands to beat London Irish.
"I am disappointed by the loss and to still be talking about it. We have some work to do and preparation to do before London Irish. It is in our hands and we have got to win next weekend."