A Securities and Exchange Commission lawsuit hasn't convinced Elon Musk to stop starting trouble on Twitter.

Just days after the agency reached a settlement with the founder of electric carmaker Tesla that allowed Musk to remain as chief executive officer, the outspoken inventor took to the social media platform to mock the regulator as the "Shortseller Enrichment Commission."

Both the SEC and Tesla declined to comment on Thursday evening.

Short-sellers, or investors who make bets that company's stock price will decline, have long been a source of irritation for the 47-year-old billionaire, and they stood to make a tidy profit when Tesla's stock tumbled in the wake of the SEC's complaint alleging Musk hadn't secured the financing he claimed for a $420-a-share buyout offer.

The case, filed Sept. 27 in U.S. District Court in Manhattan, alleged that Musk had no factual basis to support his August statements on Twitter that he had obtained funding to take the company private at a substantial premium to its stock price at the time.

The proposal, which was later abandoned, disrupted markets and harmed people who bought the stock based on the CEO's comments, the agency claimed.

While the suit compounded concerns that Musk's personal behavior is overshadowing the company's progress in accomplishing production goals and achieving a profit, analysts suggested it would damage the carmaker further if the court agreed to bar him from serving as an officer or director of any publicly-traded firm as the SEC wanted.

[Also read: Tesla production reaches record highs despite Elon Musk drama]

"The perceived 'magic' and 'mystique' of Elon Musk on the part of a large contingent of investors is a key reason the stock has commanded the lofty valuation multiples it has in recent years," JPMorgan analyst Ryan Brinkman said in a report.

The lawsuit might have limited the company's ability to raise money needed to meet its financial obligations, analysts said, particularly if it failed to meet a goal of producing 5,000 of its broader-market Model 3 vehicles per week in the remainder of the year.

"Historically, Tesla has had easy access to capital markets, largely due to the public’s perception of Musk as a visionary," said Colin Langan, an analyst with the Swiss lender UBS. "Without Musk, investors may no longer be willing to continue funding a company that has never reported an annual profit."

While the settlement, announced just two days after the SEC case was filed, resolved those concerns, it was far from penalty-free. Musk was required to relinquish his role as chairman of Tesla's board, and he and the company each agreed to pay a $20 million fine.

Shares of Tesla, which had posted an operating loss of $2.72 billion in the 12 months through June alone, took a beating.

The stock fell 14 percent, the largest drop since November 2013, in the single day of trading between the lawsuit and the settlement. That was roughly the same size as the gain made after Musk's tweet about going private in the middle of the day on Aug. 7.

The automaker has since pared those losses, and its shares are now down just 9 percent from the day the SEC suit was filed. That compares with a slight gain on the broader S&P 500.