Strike craft can engage anything in a gravity well, and the best way to manage carriers is to either send them in a circle or disable auto-attack on the carrier capital ship by right clicking on it.
I'll clarify this very good point by noting that what Zeta is saying is to right-click the attack icon, thus disabling auto-attack.
I'll also note that it's actually a really bad idea to do this with a Carrier Capital, because then they will not shoot at anything that comes within range of their weapons.
A much better way to go about this is to instead go under the Fleet control, and at the far left is the engagement range button; click it until it says "hold position".
Voila. You now have ships that will sit still unless you tell them to move, and if anything happens to come in range, the will blast it, but they won't move off to pursue.
This is also useful because even if you disable auto-attack for a carrier capital, some abilities will probably make it move around and chase things.
Which is bad.
