Hill was left beaming as Worcester secured a home win after close calls against Gloucester and Bath.
But he insisted there was still much to work on for his team and they should have scored more points in the home Aviva Premiership encounter.
"We had a poor first 20 minutes," he added. "But the last 20 minutes of the first half we came back into it and dominated that.
"We had a good start to the second half too. We deserve a pat on the back, but there is so much to work on.
"So many times we were within striking distance of the Irish try line and made such hard work of it. Maybe it is nerves; we are snatching and making the wrong decisions. But we have got a lot of work to do when we get into that 22.
"Last season we weren't getting into the opposition 22. But this year, in every game we have played, we have had so many situations inside the strike zone.
"It is now about finishing them off, we could have had another three or four tries and should have done with the amount of pressure we had near their line."
Hill also believes his team built on the second half display at Franklin's Gardens against Northampton and can look forward to the trip to London Wasps next weekend.
"I'm sure we took confidence from that," he said. "If a team lacked confidence, at 37-3 down they would have gone, the player's heads would have gone.
"But even at 37-3 we knew we were better than that, there was a hunger to score more.
"I could sense there were a few jitters tonight, we needed to get on top to settle a few nerves.
"By midway through the second half we looked like we had won the game. But I was happy to see the fourth try go over.
"We should go to Wasps full of confidence now," he added. "It is a tough place to go but we had a win down there last year 6-0.
"It might be more entertaining this year, but the players will go in confident and the dressing room is very buoyant.
"If we had lost tonight it would have been a tough week. But now I'm looking forward to Monday and coming in."