Chipotle, on the other hand, last week reported second-quarter earnings that beat Wall Street expectations. Net income rose $110.3 million, or $3.50 per share, compared with $87.9 million, or $2.82 a share, a year earlier.
Revenue increased to $1.05 billion from $817 million.
Read MoreChipotle tops Street forecasts; stock jumps
"Chipotle has been able to differentiate itself. ... It has pricing power," said Wedbush Securities' Nick Setyan. "Its business model is conducive to just moving that line faster and faster so they can drive same-store sales gains."
Panera is not in the same position to move that line faster, he added.
However, Panera is turning to technology to help improve customer service and get more patrons in the door with what the company calls Panera 2.0. It is adding kiosks and a smartphone app to allow customers to place orders, and Setyan thinks that will help.
Read MoreNew technology answer to Panera's problems: Analyst
There has been a double-digit sales lift in the markets where it is being implemented, he noted.
"It's just a matter of time until we see that being rolled out throughout the United States," Setyan said. "When it does, I actually am expecting to see same-store sales come right back."
—By CNBC's Michelle Fox. Reuters contributed to this report.