However, Warriors exploded back into life in the final quarter as Jonny Arr secured the bonus point before the impressive Matt Kvesic and Andy Goode grabbed late tries to put the seal on the victory.
The five-point haul moved Worcester back to the top of Pool A and confirmed they have made the semi-finals of the RFU Championship play-offs.
But Hill still called for his team to up their performances in the coming weeks against London Welsh and Bristol before they could contemplate a last four encounter.
"It was a bruising encounter and for 60 minutes Nottingham were very competitive," said Hill. "They were similar to that last Friday night, but then they kept it going for 80 minutes.
"They were very abrasive - which is unusual for Nottingham to be like that - and they were obviously spurred on by London Welsh's victory over Bristol last night and knew they had to try and get something out of this game. They were very competitive and we managed to pull away from them in the last quarter.
"We were better today and we are moving towards the strategy we would like," he added. "At half-time we were three tries to one up as we looked at a different type of game plan and strategy.
"There were still too many inaccuracies, missing touch kicks and knock-ons.We get a little bit excited when we get towards the try line and we have just got to make sure when we get in the opposition 22 we come away with points.
"We got a little bit better, but there were still times when we got a little over excited and as we approach these cup rugby games you have got to convert your possession and territory into points.
"It took us 60 minutes to break them down and that is probably going to be the case against most teams. A little bit of superior fitness and quality off the bench saw us end on a good note."
Hill also praised the performances of young half back duo Joe Carlisle and Jonny Arr as they kicked intelligently as Warriors looked to play the game in the visiting half.
"We need to use territory better," he added. "Joe Carlisle was putting the boot down and the crowd were crying for him not to kick it, but we won the kicking battle in the first half and it is important to play territory.
"I was pleased with Joe's first half performance, putting the ball in the corners with some nice kicks and Jonny Arr also did that.
"Yes, the backs and the wingers, Marcel and Miles, are shouting for the ball. But the reality is, against good defences, that is a high risk strategy and as we approach the semi-final stage we have got to be a bit more pragmatic and cut out the risks in our game. It is a shame, but that is what we are moving towards now.
"However, I was pleased for the crowd that they got a few nice tries at the end to put the gloss on it and that is what we want. Hard graft for 60 or 70 minutes and then a few nice tries in the end."