However, a sensational final 16 minutes saw Warriors score 28 unanswered points through tries from Jonny Arr, Josh Matavesi, Josh Drauniniu and final minute score from Ollie Hayes to claim a try bonus point.
Fly half Andy Goode then held his nerve to slot a conversion from out wide to secure another point to complete a topsy-turvy afternoon for Hill's men.
Hill said: "At 37-3 down I was thinking it was going to be a difficult week with a big game against London Irish on Friday, but that comeback has lifted the morale and dressing room.
"I am annoyed about the first half; we got well and truly beaten. But we showed real good character to come back and score four tries.
"It was a special second half for us and I was delighted. We played some good stuff and we looked a good side.
"We put some attacking players on the field that can carve up. Jonny Arr is quick at nine, Josh Drauniniu has quick feet to beat people and Josh Matavesi opens up the midfield.
"We picked a side initially to try and cope with the heavy Northampton pack, to try and stop the scrum and the drive. That was the tactic but clearly that didn't happen, we couldn't cope with their scrum or lineout.
"Making those substitutions and bringing on players that we know have got a little bit more attacking flair seemed to do the trick.
"I think the Northampton coaches were a little bit worried," he added. "If it had gone on for another five minutes we might have sneaked it, but they had taken their foot off the pedal.
"However, to come here and score 31 points and four tries, we also scored 26 points at Welford Road, is a good sign.
"We only scored 23 tries in 22 games last year. The difference this year is that we know have the capability to open up defences and score tries."
Hill also believed the 'Franklin's Gardens factor' had played a part in the Worcester display as they were dominated by an impressive opening 40-minute period from Saints.
"We tried not to get that Franklin's Gardens factor when you come here and show too much respect. But I think we did that," he admitted.
"We had a lot of possession and territory in the first half, but passes were not sticking and we were not accurate enough. Out lineout was not being won.
"I'm not sure if we were a little bit overawed by coming here, we tried not to get that mentality.
"We are not a team that should be losing 25-3 against Northampton on their own ground; it was a very disappointing first half. I think that is partly psychological.
"At half-time I was thinking it is because we are poor or because they are very good - it was a combination of the two.
"Northampton were very powerful up front and in the scrum, very powerful in the lineout and their runners were coming onto the play hard.
"If you are going to stop their power game you have to negate their scrum, negate their lineout drive and get around the corner in defence to meet their big runners on or beyond the game line. None of those three happened in the first half.
"When their forwards are doing that they have half backs sitting in an arm chair running the game. You cannot stop that and we were under the pump. We had to stop it at the source and we didn't do what we needed to in the first half."