"All you need is a couple of bad earnings reports and the same crowd that is in the stock now will be out as quick as can be," he said.
But Victor Anthony, an Internet analyst at Topeka Capital, said he still sees upside in the stock because it is creating value on its platform, which is just starting to monetize.
"Twitter is actually becoming more of a Web platform," Anthony said. "You see a strong ecosystem developing around Twitter with users, advertisers and platform partners. You have the television networks, you even have Comcast joining the fold."
He has a $54 price target and a buy rating on the stock.
(Read more: Comcast rolls out remote control accessed through Twitter )
"So strong network effects, a strong ecosystem developing around them—I think has the same kind of competitive moats that you would see from Facebook and Google ... longer term," Anthony said.
The problem, Damodaran said, is that Internet companies such as Facebook, Google and Twitter are relying on ad revenue. As more join the space, there will be less money in the ad pool to support them.
"I feel like Bill Murray in "Ground Hog Day" because a year and a half ago we were talking about another really interesting social media company with a big user base," he said. Now we are talking about Twitter. I wager in about six months we will be talking about Pinterest and Snapchat using exactly the same terms."
"Somebody has got to be adding up all these projected revenues and telling me where the online advertising market is going to be able to sustain all these companies at the same time," Damodaran said. There are going to be losers in this game. Everyone can't be a winner."
—By CNBC's Cadie Thompson. Follow her on Twitter