He knew that he'd have to face the music. He hoped for mercy. 

> *Needa had known that death was the likely consequence of his failure to capture the Millennium Falcon. **He had known, too, that he had to report the situation to Vader and make his formal apology. But there was no mercy for failure** among the Imperial military. And Vader, in disgust, had signaled for the captain’s death*
>
> <sub><sup>**[The Empire Strikes Back - Official Novelisation.][1]**</sub></sup>

He was hopeful that promptly reporting his failure would earn him some brownie-points with Vader (it didn't).

> *An hour later, brave Captain Needa boards a shuttle that takes him from his Star Destroyer to the flagship of the fleet. As he disembarks, his stomach twists into a knot. He   listens to his own footsteps echo along the glossy floors of the Imperial ship. He’s been a good captain, he tells himself. Everything will be fine.*
>
> <sub><sup>[Star Wars: The Empire Strikes Back: So You Want to Be a Jedi?][2]</sub></sup>

According to the [Star Wars Encyclopedia][3], he was driven by a sense of honour

> *When Han Solo's ship escaped, **Lorth Needa decided it would be most
> honorable if he apologized personally to Darth Vader.** The apology was
> accepted in a way, as Needa was executed on the spot by Vader's Force
> choke.*


  [1]: http://starwars.wikia.com/wiki/Star_Wars_Episode_V:_The_Empire_Strikes_Back_(novel)
  [2]: http://starwars.wikia.com/wiki/The_Empire_Strikes_Back:_So_You_Want_to_Be_a_Jedi%3F
  [3]: http://starwars.wikia.com/wiki/Star_Wars_Encyclopedia