However, Hill insisted his team should have scored even more points in the first half as a try from Andy Goode was ruled out for a forward pass after neat interplay between David Lemi and Josh Matavesi.
He said: "I am not being overly optimistic when I say this, and I would stress that I am really disappointed with the defeat, but I can see there are signs that we will get better and better.
"Bath had the best defence in the league last year and they have added to that with Mike Ford joining them, they should be good.
"To get one try was good and we created a great chance just before half-time. I think Josh Drauniniu also dropped one when Shaun Perry looked to put him away.
"We created a few chances - and you are not going to score too many against Bath - but we had an opportunity before half-time. We should have been 20 points up with the amount of possession we had.
"I saw plenty of positive signs there," he added. "It is difficult to play a lot of running rugby against a team that work purely on a strong kicking game and good chase.
"It's hard when they don't run in their own half and don't give you the opportunities like we were doing to get a holding penalty.
"But I saw enough that there was some good attacking ambition and shape.
"We are encouraging the players to stay on their feet, although one or two are still going to ground.
"Matt Mullan, Semisi Taulava, Aleki Lutui, Chris Jones, these players are beginning to understand what is required and it is not being tackled and going to ground. It's having the ability, with a good leg drive, to go through the contact.
"We have still got some players to come back in, exciting players like Jon Clarke and Nikki Walker, so there are reasons to be positive."
Hill also praised the performance of new Number Eight Semisi Taulava who was impressive on his Aviva Premiership debut.
"Semisi has settled in very quickly to life here. He is a big powerful man and takes some stopping. He is going to be very effective," said Hill.
"Semisi has come a long way and we have watched what he did at the lower levels. We saw him do it at Rotherham and the question was could he do it here. He has shown against Cardiff Blues, Llanelli Scarlets and Bath that the answer is yes."