The situation is not unlike Snap, which has seen shares languish below their IPO price amid slower-than-expected first-quarter user growth.
"I think Mark [Zuckerberg] and Facebook have been very smart about the way they've thought about this space," Costolo told CNBC's "Squawk Alley" on Thursday.
"Instagram is the platform through which they are really going after Snap. And then they've got Messenger and the messaging applications, that's where they can do more bot testing with customer support and purchases. And so they've got these pieces that support each other, that they can use to advertise and promote each other. It's an extremely powerful position to be in," he said.
After leaving Twitter, Costolo quickly jumped into his next act as CEO of fitness start-up Chorus. He's also a technology investor at Index Ventures. He said the issues faced by Snap are part of a worrying trend in technology, where established giant companies like Facebook, Alphabet, Apple and Amazon make it hard for newer public companies to get a foothold.
"You've got this real separation that the hyperscale companies ... are getting right now," Costolo said. "Blue Apron, ... Fitbit and others are really struggling to escape the levels at which they offered."
That can make it tough to attract top engineers who are looking for companies where their stock-based compensation will grow, Costolo said.
It's even an issue facing big media companies competing against Amazon or Alphabet's YouTube, he said.
"It's rough. You've got companies like Netflix, like Amazon, that can bring billions of dollars to bear on content," Costolo said. "You don't have to always pick winners, you can just make a lot of picks. With shareholder constraints, it's a lot harder to do that."
As Facebook, Twitter, YouTube and Netflix start to encroach on each other's territory in social video, Costolo said the challenge will come with consumers that continue to tie each company to its traditional offerings, such as Google's search and Facebook's social feed.
"I think the world of Susan Wojcicki, the person who's running YouTube. She's an extremely smart and talented operator," Costolo said. "I wouldn't count them out. ... I think Susan's going to try to have it all with YouTube Red, YouTube TV, and the long tail trunk of content where you see Facebook competing. She may be able to do both."
Although it seems to be a battle of giant companies in technology right now, Costolo said companies like Airbnb or Dropbox could indeed stand a chance at competing.
"These tech cycles go in waves," Costolo said. "You've got a number of companies on deck that appear to be doing quite well. Those companies are setting up nicely for the next year or so. ... The advantage today is for these still private companies that can tell the stories of their private valuations."