Schmidt's comments came during a question-and-answer session with Salesforce.com Chief Executive Marc Benioff. Schmidt stepped down from the Apple board in 2009, as Google continued to encroach on Apple's businesses with Android and Chrome OS.
Updated: The original Bloomberg story contained a misquote and was later updated to fix the error. AppleInsider has updated its story accordingly.
"I was on the board until I couldn't stay on the board anymore," Schmidt reportedly said.
Once close partners, Apple and Google have become fierce rivals since devices running the Google Android mobile operating system began competing with Apple's iPhone.
"We did not enter the search business; they entered the phone business," Jobs allegedly said of Google during a company meeting in 2010. "Make no mistake, Google wants to kill the iPhone. We won't let them."
The Google chairman of Google also offered praise about Apple co-founder Steve Jobs, who recently resigned as CEO.
"It's certainly the best performance of a CEO in 50 years," Schmidt reportedly said. "We've all benefited from the tremendous innovation at Apple. And I say this as a very proud former board member at Apple."
Earlier this year, Schmidt was replaced as Google CEO by Larry Page, one of the founders of the search giant. Schmidt now serves as the company's executive chairman, handling deals, partnerships, customers, business relationships, and government outreach.