Andy Puzder: This is the 'biggest challenge' facing the restaurant industry

Andy Puzder
Cameron Costa | CNBC

Andy Puzder may have stepped down as CEO of CKE Restaurants, but he still has a finger on the pulse of the restaurant industry.

"Really, if I were staying on as CEO at CKE, I think my biggest challenge would be to determine how you adjust to the different way people are purchasing things," Puzder said Tuesday on CNBC"s "Squawk Box."

Puzder, whose last day as CEO was Monday, said shifts in how millennials purchase everything from clothing to groceries has reached restaurants. Chains like Panera and Starbucks have incorporated mobile order and pay options, while McDonald's now has digital kiosks.

Of course, these digital innovations haven't come without growing pains for companies. Starbucks, which has seen great success with its mobile order and pay app, reported in January that an increase in digital orders actually hurt its same-store sales. Congestion at the hand-off counter caused incoming customers to leave without making a purchase, despite lines at the register being short, Kevin Johnson, Starbucks' president, and soon-to-be CEO, said at the time.

Puzder said he started to see a shift in consumer purchasing habits in June or July 2015, and that will only continue in the next decade.

"You could see retail significantly changing over a five- or 10-year period, and the companies that can adjust to that will survive and the ones who can't will not," he said.

In order to transition into this new economy, Puzder said people need to change the way they look at education, and more people need to go into vocational training, technical training and on the job training.

"You need to get people prepared for the jobs that exist," he said. "And while we're doing that, you shouldn't eliminate the jobs that they can get now and learn the skills they need to move up that ladder of opportunity."

Puzder said companies need to invest in entry-level positions to properly train the next generation workforce.

"Please don't price young people out of the labor market," he said. "When you do that you hurt them, you hurt the economy, and they don't get the training that they need."

Puzder withdrew his nomination as President Donald Trump's Labor secretary in February in the face of negative news reports.