"It's not particularly fortuitous timing, but it is what it is. We're dealing with it right now and we're following up on that," Costolo said in an interview on CNBC's "Squawk Alley." He added that it was not "a particularly pleasant experience."
The Nasdaq acknowledged on Wednesday that shareholder.com had "inadvertently" released Twitter's results early. Figures hit Twitter's investor relations page for about 45 seconds after 3 p.m. ET on Tuesday, and financial data service Selerity sent out accurate numbers in a series of tweets. Trading in Twitter's stock was halted, and the shares were battered when they reopened minutes before the bell.
Twitter reported first-quarter earnings that beat Wall Street's estimates, but revenue fell well short of expectations. Sales jumped 74 percent year over year but failed to meet the torrid growth rate the company had seen in previous quarters.
The social media company's stock suffered its second-worst day ever on Tuesday, shedding 18 percent. It continued its slide Wednesday and was trading more than 5 percent lower.
Costolo partially attributed the sluggishness to Twitter's direct response advertising business, despite its overall ad revenue jumping 72 percent year over year. The company is working to increase engagement and targeting for the ads.
"We just need to keep grinding away on our DR products and we'll get there," Costolo said.
He noted that Twitter will now only charge when a user clicks into the advertiser's site, when it had previously charged for any engagement like a retweet or favorite.
Costolo also touched on Twitter's pessimistic guidance for the rest of the year, including a warning Tuesday on monthly active user (MAU) growth in April. The company is "just not seeing the trends" it saw in the first quarter, when MAUs hit 302 million, up 18 percent year over year.
"We don't know what May and June are going to bring," Costolo said.
He noted that Periscope, the recently launched app that allows users to stream video to their followers, marks a bright spot for the company. Persicope has already hit 1 million users, Costolo said.
He contended that the app will not cannibalize Vine, the short-form video service that Twitter owns.
"Not only can they coexist, I think they make each other better," he said.
Costolo also downplayed speculation about his future at the company, noting he needs a "thick skin" in his position.
"We're going to ignore the external noise and focus and execute," he said.