"As we look at what's going on in our country today, we need to drive job growth, we need to drive GDP growth. ...We need tax reform," Robbins said in an interview on CNBC's "Squawk on the Street."
"This country needs to focus on the things that actually unite us and have united us from the beginning and have made this country great and stop focusing every day on the things we disagree on," he added.
On Wednesday, several more members of Trump's advisory councils announced their resignation in response to the president's comments on the violent white nationalist rally in Virginia that left a counterprotester dead. The departures prompted Trump to eventually dissolve the councils entirely.
Robbins said he spoke with many of the CEOs while they were on the advisory councils.
"Everyone one of these CEOs has to make a personal decision based on their company, their own conscience and what they believe," he said. "And I think that's what all of them have done."
Robbins said "it is incomprehensible that we're having this conversation in 2017" and said Cisco denounces "racism, discrimination, neo-Nazism, white supremacy."
Cisco released earnings for its fiscal fourth quarter on Wednesday. The report showed revenue, which was down 4 percent year over year, has now declined on an annualized basis for seven consecutive quarters. It posted in-line results and better-than-expected sales.
Robbins said Thursday that the company is bringing forward a "cycle of innovation" and investors will see that continue for the next few years.