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GoDaddy CEO: Yes, the IPO was great, but ...

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Despite a successful opening at the New York Stock Exchange, Blake Irving, GoDaddy's CEO, said Wednesday the company still has a lot of work ahead of it.

"The market is treating us well, but that's just today. We've got to deliver quarter after quarter ... [Wednesday] is an important day, but it's just a milestone," Irving said in an interview with CNBC's "Squawk on the Street. "

He made his remarks after the Web hosting company debuted at $26.15 per share, about 30 percent higher than its initial public offering price. In midday trading Wednesday, the stock was at $26.23 a share, up 31 percent. Click here to see where it is trading now.

Ahead of the IPO, some investors and analysts were skeptical as the company has yet to post a profit. "I think it's telling that it's not making money," Jim Cramer said earlier on "Squawk on the Street." "That's code for 'what the heck are they doing?'"

Nevertheless, Irving added that "if you actually look at the free cash flow we kick out … we are a great business. We pay for everything upfront and we have to amortize our cost overtime, so that always creates some gap weirdness."

With regard to the timing of the IPO, Irving said the higher demand for GoDaddy's services as well as the recent technological leaps made this the ideal time for it, as opposed to 2006. "The state of small businesses is very acute," he said. "The tools in 2006 were not there. Technology has advanced a lot since then."

The state of IPOs

IPO pipeline extensive: NYSE's president

GoDaddy's offering came in at a time when the IPO market had slowed down considerably.

On Tuesday, a report from Renaissance Capital said that 34 IPOs raised $5.4 billion in this year's first quarter. Last year, the number of offerings during the first quarter was 78 and the amount raised was nearly double.

"[This] is peculiar because interest rates are still low, the VIX is relatively low and stable, and the asset prices in the stock market are near all-time highs, so you'd expect [the IPO market] to be far more robust, " Tom Farley, president of the New York Stock Exchange, said in another interview with "Squawk on the Street."

Read More GoDaddy prices IPO at $20 per share; stock soars in early trading

"My theory is that you saw a burst of IPOs in the fourth quarter of last year, where you had some that might have otherwise been in the first quarter of this year," he said.

Nevertheless, Farley also said he expects the IPO market to pick up moving forward. "The pipeline is extensive. We have a lot of great companies, particularly in tech ... unless some of those underlying fundamentals deteriorate."

—CNBC's Bob Pisani contributed to this report.