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."

Sarah Goldstein, 24, found the posts two weeks ago after her claim for personal independence payments (PIPs) was turned down.
One post described how the nurse wanted to "catapult" a claimant "back to...[where] he came from".
Capita, which assess claimants for the government, said it was investigating.
Mrs Goldstein, who has fibromyalgia, Raynaud's phenomenon, and suffers with chronic anxiety, migraines and depression, claimed Employment and Support Allowance (ESA) and first applied for PIPs in October 2014.
Her husband, Jay Goldstein, said she had been assessed last year but turned down for PIPs because it was felt she was "making everything up".
Mrs Goldstein reapplied for PIPs at the end of 2015 and was assessed at her home in Ilkeston, Derbyshire, in March by the nurse, who works for Capita on behalf of the Department for Work and Pensions (DwP).
But the couple's suspicions were aroused when they found they had been turned down by the nurse on the basis of a number of "falsehoods" in her accompanying report, which has been seen by the BBC.
These included claims that Mrs Goldstein had given birth to 13-month-old daughter AJ naturally. Mrs Goldstein had a caesarean and said she was never asked about the birth.
In addition, the report said Mrs Goldstein was "calm, relaxed and her mood appeared stable". Mr Goldstein said his wife was "clearly anxious" and did not make eye contact with the assessor.
Mr Goldstein, 25, said the nurse's name was on the report, so his wife looked her up on social media "to make sure everything was above board" and discovered the posts.
One, written in July 2014, appears to attack a claimant who had lost two legs as a child and had appeared on a programme about benefits.
The post said he should "get a job fitting carpets" and that she "would like to catapult the scrounger back to...[where] he came from".
It is believed the nurse started working for Capita a few months before the July post.
Mr Goldstein said: "People need to see how people with disabilities like my wife are treated. They're human beings, they deserve a good quality of life.
"[The nurse] is clearly not the best person for that job."
The couple reported the posts to Capita, which, as a result, suspended the nurse and told the couple a new assessment on Mrs Goldstein would be carried out on Wednesday.
Mr Goldstein said his wife, had been left "stressed" and "unwell" over the claim.
A Capita spokesman said: "The individual was suspended as soon as we were made aware of the allegations, and further investigations are taking place. All prospective assessors are subject to strict security and vetting checks. We also have strict policies in place which govern the use of social media."
In response to a request for a comment, the nurse told the BBC to contact Capita.
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.
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A disability benefits assessor has been suspended after allegedly posting abusive comments about disabled claimants on Facebook.