The Robins have lost 11 of their past 12 league games, winning just once in that time, and are 20th in the table - two points above the relegation zone.
"It is a horrendous statistic," Johnson told BBC Radio Bristol.
"I'm ashamed of that. It hurts. We have to keep fighting."
Former Barnsley boss Johnson arrived at Ashton Gate in February 2016 and steered Bristol City clear of relegation last season.
A promising start this term saw his side occupy fifth spot in October, but Saturday's loss at the City Ground saw them drop below Forest - who had not won since 2 December.
"It was a frustrating watch for all of us," Johnson said. "We were good in the second half and had a couple of chances we needed to take.
"The Championship was never going to be easy - we are in a rebuilding phase.
"We spoke at the start of the season about history makers and it was supposed to be positive - not bad history.
"We've got to make sure we make history in positive ways and we can still do that this year. We need to fight our way back up the table. I believe that we can."
Bristol City head coach Lee Johnson admitted he was "ashamed" to see his side set a new club record of eight straight league defeats with a 1-0 loss at fellow-strugglers Nottingham Forest.