But a late score in the first half from Scott Hamilton - and sin bin for Goode - saw the momentum shift back to Leicester.
"I thought we played well enough to win. For the first 30 minutes and throughout the first half really I felt we played some great rugby.
"We have taken a step forward with the way we want to play; we played with a lot of ambition and kept the ball in hand to play some good stuff.
"The crucial moment was the Andy Goode sin bin. That came right on the stroke of half-time and Chris Pennell had those two crucial kicks which unfortunately saw one come off the post.
"It was a vital time and I am convinced if Andy Goode had been on the field he would have slotted those two penalties over and got us going and the crowd going in the second half.
"In a game where they always say it comes down to small margins, that was the key blow and yet again we are down to 14 men.
"I know they had one too which was a bit harsh to be fair, but ours was a silly one that didn't look that bad to me. But the referee saw it in live time and decided that was the case. That cost us and it was crucial and disappointing at the wrong time."
Hill added that he had no arguments over the two penalty tries awarded to Leicester in the second half including one in the final minute to hand victory to the East Midlanders.
"I had no arguments with the try at the end - we were going backwards," he added.
"We lost a bit of ball attacking in their 22 and they turned us over and went the length of the field before getting the five-metre scrum.
"It was always going to be difficult because they have got an extremely powerful scrum. They were shunting us back so the referee had no option in that last one."