Stephen A. Smith explains that the NFL should have had the anthem protest issue cleaned up long ago, and Papa John's CEO John Schnatter has the right to voice his opinion on the matter. (2:18)

Executives from Papa John's, the official pizza company of the NFL, expressed disappointment on a conference call Wednesday about the league's ongoing player protests during the national anthem.

"The NFL has hurt us," company founder and CEO John Schnatter said. "We are disappointed the NFL and its leadership did not resolve this."

Executives said the company has pulled much of its NFL television advertising and that the NFL has responded by giving the company additional future spots. Later in the day, a spokesman clarified that the spots themselves weren't being pulled, just the NFL shield or "official sponsor" designation on those spots.

"Leadership starts at the top, and this is an example of poor leadership," Schnatter said, noting he thought the issue had been "nipped in the bud" a year and a half ago.

In revising sales estimates for the next quarter, Papa John's president and chief operating officer Steve Ritchie said on the call that the NFL deal was the primary suspect behind the decline and that "we expect it to persist unless a solution is put in place."

Ritchie said that research has found that Papa John's has been the most recognized sponsor associated with the NFL for two years running, which he said means the company's performance can track with that of the league.

Papa John's has a deal with not only the NFL, but also with 23 individual teams.

Company executives declined to disclose exactly how much money in projected sales Papa John's lost from its association with the NFL and declining ratings, which mean fewer people are ordering their product for game days, they said.

Papa John's stock was down 8.5 percent on Wednesday.

ESPN reached out to 18 NFL official sponsors in the last few days and asked the companies about its current relationship with the league and if any marketing programs had been changed due to the turmoil. Only five sponsors responded with a comment.

Verizon spokesperson Jim Gerace wrote via email that "our discussions with any partner are between us and while we haven't done anything different, we don't discuss future plans."

"We are not going to critique their performance in public just as I wouldn't expect them to critique ours," Gerace added.

A Hyundai spokesperson said in a statement, "Hyundai participated in constant dialogue with the league to discuss all aspects of our partnership, including national anthem protests. We've been pleased with the frequency and openness of those conversations."

A spokesperson for Dannon, whose Oikos brand has an official NFL deal, said: "We continue to monitor the situation carefully and have not made changes to our advertising or related plans."

Nike and Anheuser-Busch referred to previously issued statements.

League sponsors that either didn't return a message after 24 hours or declined comment included: PepsiCo, Mars, Visa, Campbell's Soup, Procter & Gamble, Castrol, Bose, McDonald's, Nationwide, Microsoft, USAA, Marriott and Bridgestone.