Hill admitted a sloppy start from his team, as they conceded two tries to England man Manu Tuilagi, had proved costly.
But he was pleased with the effort and desire shown by his men as they again showed flashes of the new attacking dimension they are keen to bring to the game.
"I actually thought we had secured a bonus point for a moment with the late try but my maths wasn't up to scratch," admitted Hill.
"To lose the tries we did in the opening 12 minutes was massively disappointing. The manner we conceded was disappointing and that put us on the back foot. But the players battled back.
"We lost Chris Pennell to the sin bin and when we get him back we lost Shaun Perry. But the character was good and when we put young lads on in the second half we kept going.
"We wanted to play with real ambition and our scrum was pretty solid so I can't ask much more from the young players.
"We would want more than one point from the opening two games and it shows the impact of what happened in our first game at home to Bath," he added.
"We scored two tries today and one last week, our attack is building and we want to score tries.
"If we do that we will win matches. To come here and score 26 points is a good effort against a very strong and powerful Leicester team who played some good rugby.
"We cannot get to despondent and look to take what we did today into the Gloucester derby game."
Hill also pinpointed the way in which his Warriors kept going until the final whistle as Grove crossed with just seconds left.
He added: "We kept going well which was important. We lacked that last season, when we had the ball we sometimes lacked urgency and enthusiasm. Now when we have the ball we look for a spark and we look to score tries.
"We will have to look at where we play our rugby. We got turned over twice early on and they scored, we have got to do it at the right times when we have numbers on.
"We are going to take some time to get it right, but to score 26 points here is a good achievement.
"I was also pleased with how the pack went," he added. "They were up against a big side and they were marginally better than us. I was pleased with our lineout work and they are good at stopping the drive.
"There was a series of scrums at the end of the first half when we held Leicester out - that was character. I was also disappointed with the penalty try at the end because I wasn't sure we were going backwards."