Hill conceded after the game that a faltering lineout had not helped the visitors and felt that a run of testing away games against Sale Sharks, Harlequins and now Bath Rugby had caught up with his men.
"It felt like it was one game too far for us in this spell," he said. "We have put a huge effort in the last few games and been away from four of the last six games.
"We have had to put a lot of effort in each week. We started brightly but we ran out of steam and the intensity wasn't at the normal level. Consequently our defence was under huge pressure.
"The mind was willing but I could see this was going to be a dangerous one. We looked on current form and Bath would have been third in the league over the last five matches so it was always going to be tricky.
"The replacements gave us more energy and it was good to score the second try; that was a little bit of consolation. They had a go and gave us life, but today defence and lineout was very disappointing.
"Our lineout could not function and we got into some positions and lost the lineout, it just let Bath off the hook. You have got to take your chances.
"We made some errors in the first half that cost us too. A free kick from a scrum in our 22, they get the ball and score from it. The set piece, unusually, didn't function and we didn't get the edge in the scrum and the lineout stats were not good.
"We allowed Bath some clean possession of their lineout and we know they have got some good moves, it was difficult for our backs to defend with two distributors facing them with (Olly) Barkley in at centre.
"I was pleased with Kai when he came on, he added energy," added Hill. "Most of the replacements did that, the starting 15 were a little bit tired and those that came on were sharper."