Lefkofsky told CNBC that Groupon was "misunderstood" during Andrew Mason's tenure, although he said that the founder himself didn't create a discount in the stock price.
"We absolutely didn't manage the process of being public as well as we could have or should have," Lefkofsky said Thursday. "We're now just intensely focused on the day-to-day business. Hopefully we'll be less misunderstood over time."
Leonsis said that though Mason remains well respected in the company, "the board just reached a point where we felt that bringing in some new leadership who had managed a global enterprise was the right step."
The stock price has risen nearly 50 percent since Mason's ouster in late February.
Groupon is taking its time to consider CEO candidates and will begin the formal search in June, the two said. "We would rather be deliberate and thoughtful and bring in world-class talent at the right pace," Leonsis added.
(Read More: Groupon's Fired CEO Mason: the High and Lowlights)
Although the stock remains far below its IPO price, Lefkofsky maintains a long-term view. "I'm going to be a shareholder for a long time and so the question is not what it's worth today or this quarter, it's what it is worth over a long horizon," he said.
Leonsis said that inside the company, there "isn't a lot of focus on stock price within the company. Most of the focus and attention is on main street, merchants and customers. Most of the discussion is how we meet our expectations. If we can continue to do that, our numbers will speak for themselves."
Earlier this week, a report surfaced that Leonsis expects Groupon to reach $100 billion in revenue. When asked about this, he said that "sometimes media is in the entertainment business" and that the comment wasn't intended as it was portrayed.
(Read More: Groupon's Q1 Earnings: Revenue Beats Forecasts)
"It sounded like a salacious comment, and it wasn't meant to be," Lefkofsky said. "The comment was, 'We're not focused on being at the current billings we're at today. We're trying to figure out how we get to 10 times or 20 times that size,' " he said.
"We sit at the intersection of mobile and local, which is probably one of the greatest places you can be, if you can get that right," Lefkofsky said. "I think we have the chance to be the first e-commerce company of scale that is predominantly mobile. It's a huge opportunity."
The co-CEOs said Groupon operations are undergoing a fundamental change as it looks to gets customer to interact with it as a mobile market rather than buying daily deals.
Groupon is "moving from being a predominantly push email experience to a marketplace where people can come down and pull deals," Lefkofsky said. Email now accounts for only 45% of its business, he said, adding that "more and more, we're trying to change consumer and have them come (to Groupon) when they have a demand."
(Read More: Groupon and Zynga shares up on Jana's investment)
Its consumer base is also changing, skewing female and increasingly affluent, according to Lefkofsky said. "The heart of our customer is a 42-year-old female with two kids," he said.
Groupon's international business has been a drag on the company, which has been challenged by a weaker online community, Lefkofsky said. He said he's concentrating on generating strong consumer and merchant satisfaction, as well as transferring North American technology to Europe, which he sees as a key factor to success in that region.