Kevin Davies put his old club behind after 93 seconds and Rovers had goalkeeper Paul Robinson to thank for Bolton not inflicting further damage in a half they dominated.
A more even contest was on display after the break, but Jordan Rhodes' late header was mere consolation after Lee Chung-Yong doubled Wanderers' advantage.
"To start the game like we did was very, very surprising, I must admit," said Rovers boss Berg. "We're playing a local derby, we're playing against a team we played in the Premier League last season and we give them that much space.
"They played in front of us, they played in-between us, they played behind us, they scored a goal. For us to expect to win the game by starting that way is very frustrating, very surprising and nowhere near where we want to be.
"We have enough experience to know that when we start the way we do we give ourselves a mountain to climb and at the moment we're not good enough to get back into it."