Four second-half tries blew the game apart after the west country rivals had been level at 5-5 after 50 minutes and even if Bath fail to reach the semi-finals coach Booth believes his side proved a point as they continue to show signs they are on the rise.
"We are in for the long haul and slow and steady improvement," he said. "We will see how that pans out but we have spoken about how important it is to pull on a Bath shirt in any competition and we have tried to instil some pride into wearing the shirt. I think you saw that today."
He added: "You saw the importance in the fixture - not necessarily in the competition sense but to the two clubs - in the quality of sides that the two clubs put out and that is important in building the way that Bath are trying to move forward."
Booth believes his side could have added even further points after they had tries disallowed in the absence of the television official.
"Although the scoreboard doesn't show it, we were held up over the line twice if not three times," he said. "It is a topic for another day but if there was a TMO, it might have been a different result in the first half."
Gloucester assistant coach Carl Hogg warned his squad there will be some "harsh words" at Monday's first training session of the week as they prepare for a top-of-the-table Aviva Premiership clash with Saints.
Hogg said: "At 5-5 with 20 minutes to go, we were still in it but I think the players didn't adapt to the referee's interpretations. Conceding 17 penalties in a game and having two yellow cards means you are always going to put yourself on the back foot.
"Although we defended very well in the first half and, at 5-5, I thought we had weathered the storm but it took its toll in the last 20 minutes. When you are asked to defend for so long as we were during the first half, it is going to take its toll. It is difficult to take to concede so many points.
"It was a local derby with a lot of pride at stake but essentially we couldn't move through the competition. We have just got to use this as motivation moving forward."
- Sports & Recreation