However, Worcester were forced to dig deep and twice fell behind to the battling Dragons in the game before 26 stunning unanswered points in the final quarter secured a bonus point win in Pool A.
"These play-offs, as much as we would like to play 80 minutes of superb rugby, we have got to realise we are playing against some very good opponents. I though London Welsh were excellent in the first half," said Hill.
"We will find ourselves under pressure and we will need to dig deep at times and show huge character.
"What I was pleased about today was, even if the tactics were not carried out as they should have been, the character of the players to come back from a tricky situation and wrestle the initiative away from London welsh was a big step for this group of players.
"The first 60 minutes was uncharacteristic of us and we didn't stick to the game plan," added Hill. "It is very simple - if we do what we are supposed to do then we are very good.
"It wasn't until the 56th minute that we did what we said we were going to do so we will need to have a serious chat about that on Monday morning.
"We said we would take them on through the guts, be very direct and get the heavy artillery to batter them through the forwards because they have got a very good press defence. But for 60 minutes we ended up just trying to ping it wide.
"Even the first scrum we had in the second half, after we had a chat in the dressing room, what do we do? We move the ball wide and Chris Pennell failed to take pass and then we are under pressure.
"It wasn't until the 56th minute that the penny dropped. It took two replacements, in Bruce Douglas and Greg Rawlinson, to take it by the scruff of the neck and take us forward. Greg carried superbly and people suddenly realised that was what we were supposed to do.
"It was a nervy and disappointing performance for almost an hour. As soon as we did what we said we were going to do we scored 26 unanswered points and looked outstanding. We were pretty faultless in the final quarter.
"It looks good on paper, but at 14-13 at half-time it didn't look like we would get the bonus point. However, we did show great character so that is a positive."