Andy Goode dragged Worcester back into the game before half-time before a frenetic second half and rollercoaster final five minutes saw Kai Horstmann grab a late try and Joe Carlisle hold his nerve before Blues missed a drop goal in the dying seconds.
Hill admitted that nerves and a high penalty count had almost cost his Warriors the ultimate price.
He said: "We started off poorly, just the way we didn't want to start off. We were too anxious and piling into the breakdown and committing penalties. Bedford were playing cup rugby and taking the three points.
"That gap, when they scored the try, saw our players suddenly become very anxious. The jitters came and we made lots of uncharacteristic errors. I haven't seen us make those kind of knock-ons and lose that much ball in contact for a long time.
"I thought Bedford came with nothing to lose with no pressure on them at all. Because of that you could see they were much more relaxed, they hardly dropped a ball and everything they did came off.
"What we saw was a lot of pressure on the Warriors and we made those errors. We know we have escaped and I would hope we won't play as badly as that in the final.
"I don't think we could have argued if Bedford had won," he added. "We had enough possession in the second half but we didn't establish control and weren't as dominant up front as we needed to be.
"We have seen the Bedford pack improve and their lineout was good and they stopped our drive. The one area where we did well was in the scrum.
"Our lineout didn't function as well as it normally would to get the platform, again down to nerves, but we have got to sort that out as we can't afford to go to Cornish Piartes or London Welsh and play like that in the final."
Hill revealed a rally cry from experienced campaigners Horstmann and Goode at half-time helped stop the penalty count rot.
But the Head Coach admitted the team were still too anxious to score straight away in the second half and lacked composure.
"Goodey and Kai spoke well at half-time, we sorted the defence and tackle. If it is a tackle you can go and contest it, but when it becomes a pile-up you have got to leave it and we were throwing too many bodies at it," said Hill.
"In attack, though, we needed to be more accurate. For me, on the touchline, when we got into the red zone we looked to score a try very quickly. We were pinging fast passes around and it was being spilt.
"I tried to get the message on numerous times. It doesn't matter if you go through 35 or 40 phases. If you go yard by yard and score seven points that is all you need. That is what we needed in the last 20 minutes.
"I never lost faith," added Hill. "Fortunately I had someone on the touchline telling me how many minutes were left and although the clock scored more than 80 minutes I had faith that we would win the game.
"I never got anxious, the only time I was jumping up and down was when we were winning by a point and were fiddling around with it on the halfway line."