"Look, you've got executives leaving, he doesn't have a lot of backup, there's not a succession plan. He's super busy and exhausted, but he has time to do this podcast and smoke weed, or whatever it is, and drink whiskey. And he's missed tons of deadlines," said Tengler, who is chief investment officer at Heartland Financial.
"The valuation reflects a company that's operating at top speed and is delivering on every level, and I just don't see it. I think there's a lot better places to be invested," she added Friday on CNBC's "Closing Bell."
Musk took viewers by surprise late Thursday when he smoked marijuana and drank whiskey during a 2 1/2 hour livestreamed interview with comedian Joe Rogan. The two engaged in a lengthy discussion on a number of issues including humanity, artificial intelligence, Tesla, China and Musk's social media habits.
"I think it's on balance more good than bad, but there's definitely some bad, so hopefully the good outweighs the bad," Musk said Thursday of his Twitter use.
Following the appearance came news of the resignation of two leading Tesla officials. Tesla's chief accounting officer, Dave Morton, resigned after just a month, citing "the level of public attention placed on the company." Tesla's chief human resources officer, Gaby Toledano, took a leave of absence in August after 15 months on the job. She announced Friday morning that she would not return to work at the company, according to Bloomberg.
Tesla shares nosedived Friday, falling 6.3 percent to $263.24 during regular trading.
Tesla bull Eric Schiffer, chairman and CEO of private equity firm Patriarch Organization, said the executive departures are likely driving the stock's decline. While Musk's behavior doesn't do him or the company any good, his antics are largely priced into the stock, he added.
"These kind of clips don't help in the short run. But I also think a big component of Musk is built into Tesla. Most of the core investors, they recognize they're dealing with this eccentric, unusual figure, and I don't see many of them bailing," Schiffer said during the same "Closing Bell" interview as Tengler.
Oppenheimer Tesla analyst Colin Rusch attributed Tesla's decline to Musk's behavior and the possibility of a Securities and Exchange Commission investigation of Musk's August go-private tweet that alleged he had "funding secured" for the maneuver.
"The real concern weighing on the stock here is not just Elon's behavior, but Elon's behavior coupled with the potential of an SEC investigation," Rusch said on CNBC's "Power Lunch." "And certainly when you see two [officials] leaving in the space of a couple months, that's not a great signal out to the market."
Rusch said now is the time for the Tesla board to step in and build up the company's leadership team, adding that the board needs to "bring in additional expertise and voices to help this company execute and have a public face to investors that they can trust."
The board has "not proven they can handle Elon when he's moving towards the downside of his behavior patterns. This is the point where they prove their worth to the company. It's now or never, in my view," Rusch said.
He said whether Musk is still fit to lead is a "major question."
For her part, Tengler didn't discount what Musk has done for the company but said she fears his deleterious effects on the stock.
"You start to add up the cumulative effect of all these actions, and you say: If this whole company's valuation is dependent on one person, that's not investing to me, that's gambling. So I find there's better places to be. I get the vision, I love the car. I think everything that he's done has been exceptional, but I think the wheels are coming off, and we're watching it in real time," Tengler said.
Tesla did not immediately respond to CNBC's request for comment.