In a tribute to Walter Cronkite written for this week’s Time magazine, Tom Brokaw recalls the night Cronkite gave him some advice, after Brokaw was named anchor of NBC’s Nightly News.

“There will be nights,” Brokaw quotes Cronkite as saying, “when you think you’ve done a brilliant job on a big story. You’ll leave the studio with the echoes of praise from your colleagues ringing in your ears. And once outside in New York, you’ll realize there are millions of people in this city alone who didn’t watch and who don’t give a damn what you just did.”

It was, Brokaw writes, “a line I remembered at the end of many days.”

• Related: The AP, NYT, and Washington Post write-ups on the funeral of Walter Cronkite.

• Earlier on TVNewser: Gathering For The Funeral Of Walter Cronkite