But a late score from Dean Mumm saw Exeter - for a second successive season - snatch a late win at the home of the Warriors.
"I was delighted with the fight-back. We fought back so well and the momentum appeared to be with us. But we still l had a lot of defending to do with ten minutes left," said Hill.
"I could see us winning that game but the sin bin caused us some problems and being down to 14 men did not help.
"It was one of those games, the story of the season so far, as in the last five minutes we just missed out.
"I was pleased with our second half fight-back," he added. "We had to increase our line speed in the second half. Exeter scored two good tries, but we had sat off them so we needed to come off the line hard.
"We had to retain possession better too, we had lots of ball in the first half but we squandered it while Exeter kept it better and went through multi-phases. We were going for the miracle ball.
"We played some good stuff with good intent, the players were all confident and although we were 14-6 down we were playing well. The tactics were working."
Hill admitted he was just as surprised as everyone else in the stadium when David Lemi saw a first half try ruled out for a knock on after the Samoa ace looked to have scored.
"I couldn't see the knock on myself," revealed Hill. "It was a great cross kick from Andy Goode and really good work by David Lemi.
"The tough judge has called it and it looked a very harsh one to me. I don't think anyone in the stadium would have argued if it had been given.
"That was crucial and knocked a bit of stuffing out of us for a while, particularly as it was such a well worked try."
And he added he would look at the late yellow card to Josh Matavesi which saw Warriors play out the final ten minutes a man down.
"I didn't really see the sin bin," said Hill. "Josh thought the ball was out and I will have to have a look at it.
"It's hard enough trying to defend with 15 against Exeter because they keep coming at you and with 14 it left us stretched.
"Josh apologised to the group in the huddle at the end. Did it turn the game? I don't know, it was going to be tough but I felt we were in with a good shout."