ListAnimate evidently constructs a Manipulate, and so we should be able to replicate its behavior. One way to figure out how ListAnimate works is to inspect its InputForm (click image to inspect output):

ListAnimate[Table[i, {i, 0, 1, 0.1}], 
  AnimationRepetitions -> 1] // InputForm

What we see is that ListAnimate uses a control with an AnimationRepetitions option, namely Animator. Here's a slimmed down version:

Manipulate[i, {i, 0, 1, 0.1, 
  ControlType -> Animator, AnimationRepetitions -> 1}]

Add options depending on the look desired.

ListAnimate evidently constructs a Manipulate, and so we should be able to replicate its behavior. One way to figure out how ListAnimate works is to inspect its InputForm (click image to inspect output).

ListAnimate[Table[i, {i, 0, 1, 0.1}], 
  AnimationRepetitions -> 1] // InputForm

Unsurprisingly, ListAnimate uses a control of type Animator. The default Manipulate slider is a Manipulator (and Slider is distinct from both). If we specify an Animator in Manipulate, then we can use the AnimationRepetitions option. Here's a slimmed down version:

Manipulate[i, {i, 0, 1, 0.1, 
  ControlType -> Animator, AnimationRepetitions -> 1}]

Add options to achieve the appearance desired.