What's worse, failing Darth Vader or having to apologize for it? Captain Lorth Needa was in that most terrible of positions when his Star Destroyer, the Avenger allowed the Millennium Falcon to escape pursuit after the Battle of Hoth.
Ingeniously, the Falcon never really escaped as Needa surmised. It was a daring maneuver executed by her pilot, Han Solo, that caused Needa to think so. Solo charged the Star Destroyer at attack speed. At the last possible instant, he cut speed and power and settled his ship in a blind spot on the Avenger's conning tower. The ship effectively disappeared from Imperial scopes, just as Lord Vader requested an update on the pursuit from Needa.
Gathering his courage, Needa went to Vader's flagship, the Executor, to apologize to Lord Vader personally.
Vader accepted Needa's apology ... and killed him.
Captain Needa was the second Imperial officer to die by telekinetic strangulation in The Empire Strikes Back. In the X-Wing novel series, we learn that a relative of his is in charge of operating a giant orbital solar mirror over Coruscant.