Oakland City Councilwoman Desley Brooks filed a complaint against her own city and the city attorney Tuesday, alleging they failed to adequately defend her in a legal battle with ex-Black Panther leader Elaine Brown that cost Oakland more than $2 million.

The claim contends that City Attorney Barbara Parker and her staff neglected to present evidence at trial that would have been favorable to Brooks and detrimental to Brown. The case stemmed from a fight in 2015 between the two women in a Jack London Square restaurant over an affordable housing project that Brown wanted the city to fund.

Jurors ordered the city to pay Brown $3.75 million for elder abuse and injuries she suffered, saying that Brooks was acting in her capacity as a city official during the altercation. The jury wanted Brooks herself to pay $550,000.

But a judge, who found that Brooks repeatedly lied under oath, later ruled that those amounts were excessive and lowered them to $1.2 million and $75,000, respectively. The city had to pay an additional $1 million for Brown’s legal fees.

Dan Siegel, an attorney for Brooks, said the city attorney’s office was ill prepared, negligent and incompetent in its handling of the suit.

The claim accuses Oakland’s attorneys of failing to use evidence about Brown’s intoxication that night as well as threats she allegedly made against Brooks.

Alex Katz, a spokesman for the city attorney, said the office handled Brooks’ defense professionally and diligently.

“It is not surprising that she is unhappy with the judge’s ruling that she committed perjury, with the judge’s and the jury’s findings of fact, and with their $75,000 punitive damages award against her personally,” Katz said in an email. “It is unfortunate that her claims are full of inaccuracies and falsehoods. Of course, we will treat her claim like any other and respond at the appropriate time.”

Brown’s lawsuit alleged that Brooks knocked her backward over a stack of folding chairs in the restaurant, Everett and Jones BBQ. Brown underwent surgery for a torn rotator cuff and reported the incident to police, but prosecutors declined to file charges.

Brooks has said she acted in self-defense, pushing Brown away after she poked the councilwoman, though the judge and jury concluded Brooks gave false testimony.

“Overall, the quality of the representation provided by respondents was far inferior to what should be expected in a high-profile, high-stakes case,” Brooks said in the claim.

If the city throws out her claim, Brooks will file a lawsuit against the city, Siegel said.

The complaint doesn’t specify the amount of damages Brooks is seeking from the city. It alleges she “suffered an unjustified award of monetary damages, grave harm to her reputation, and extreme emotional distress” because of Parker and her deputies.

Brooks, who represents part of East Oakland and was first elected to the City Council in 2002, is facing a slate of four challengers who are trying to unseat her in the November election.

Kimberly Veklerov is a San Francisco Chronicle staff writer. Email: kveklerov@sfchronicle.com Twitter: @kveklerov