HOUSTON -- Joe Biden's campaign offered a warning to the former vice president's 2020 Democratic primary rivals after Thursday night’s debate: “Attacking Joe Biden is not the way to advance yourself in the polls.”

From the spin room at Texas Southern University in Houston on Thursday, Biden campaign officials briefed reporters after what they called a “stellar night” and “forceful, passionate performance” from the party's frontrunner.

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“I think candidates have seen, not just in the debates, but over the course of this campaign, that attacking Joe Biden is not the way to advance yourself in the polls,” Biden deputy campaign manager Kate Beddingfield said after the debate. “I do think candidates are seeing that, and learning that lesson in terms of where we are in the race.”

Prior to Thursday's debate, the campaign told reporters that Biden had “a target on his back” as the frontrunner, after grappling with sustained critical media coverage and a narrative from his left flank that he’s not progressive enough.

But during Thursday night’s debate, it was former Housing and Urban Development Secretary Julian Castro who attempted to bash Biden — this time, seemingly hitting him on his age and memory.

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Castro took a shot at Biden’s memory, accusing him of contradicting himself about whether Americans would have to buy into a public health care option under his plan or if they would be automatically enrolled.

“I can’t believe that you said two minutes ago that they had to buy in, and now you’re saying they don’t have to buy in,” Castro said. “You’re forgetting that!”

Castro’s comment wasn’t accurate, as Biden, just minutes before stated: “Anyone who can’t afford it gets automatically enrolled in the Medicare-type option we have.”

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Biden adviser Anita Dunn checked Castro, saying that his “cheap shot” was “based on a lie.”

“I think Castro, who likes to talk about learning from history, clearly didn’t learn from the first two debates that taking personal cheap shots at Vice President Biden actually doesn’t work out that well for the candidate who throws the shot,” Dunn told reporters. “It’s unfortunate that Castro decided to go the route he did.”

Meanwhile, the campaign said Thursday’s debate was an important exchange about policy, and that voters now know more about the candidates. Dunn touted Biden’s performance, saying that Biden’s persona on Thursday was that of “Joe Biden the statesman,” citing his empathy toward other candidates on stage over a series of issues.

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“His final answer on resilience really did illustrate why people really have a real connection with Vice President Biden and why they feel he gets their lives and why they could trust him,” she said.

And Biden senior adviser Symone Sanders added that “voters know Joe Biden.”

“They know him, they know his record, they know he’s been there for them,” she said. “So the asserting anything that flies in the face of what the voters know to be true themselves because of their experience with Vice President Biden just won’t stick.”