Opponents Bucuresti lost 106-3 to Gloucester in last season's competition, but Bristol toiled for a 27-3 success and required two second-half tries from Brian O'Riordan to give them a degree of breathing space in Romania.
"We were up for it, but we were sloppy," said Hill. "Bucuresti were strong, and they make life hard for you.
"We made quite a few changes from last week, and we didn't click.
"We thought we could run the ball and score 12 fantastic tries without doing the hard work, but you can't do that at this level. We went away from our game-plan.
"I don't know if it was complacency - I honestly don't know what the reason was. We should have won by a much bigger margin."
Bristol still managed a bonus point success though, to join Pool One leaders Newport Gwent Dragons on five points, with Sam Cox, Marko Stanojevic and Luke Arscott following O'Riordan over the Bucuresti line.
Worcester, who face a tough Pool Five encounter against in-form French side Clermont Auvergne next Saturday, overcame Sixways visitors Viadana 25-7 with props Chris Horsman and Lee Fortey claiming tries on route to a bonus point.
Worcester though, did not score during the final 30 minutes, leaving rugby director John Brain to bemoan his side's poor finishing.
Elsewhere, Narbonne shaded a tense Pool Two encounter 19-16 against GRAN Parma after fly-half Christopher Ruiz landed a 72nd-minute penalty.
Parma matched their opponents blow for blow, but Ruiz's kicking proved the difference as Narbonne gained an important away success before hosting Saracens next weekend.
And tournament newcomers Albi made a promising debut in losing 30-21 at home to Clermont Auvergne.
Albi's Welsh fly-half Cerith Rees touched down, as did full-back John Stewart and wing Fa'atonu Fili, but Clermont playmaker Alexandre Peclier made a significant contribution, kicking 15 points.
Peclier converted all three Clermont tries from Thomas Combezou, Raphael Chanal and Pierre Vigouroux, while his late penalty strike also denied Albi a losing bonus point.