If you're going against technologically superior energy-equipped ships, you've got three main routes to defeat them:
1) Overtuned engines - you need enough speed to get into your range, punch up those speed modifiers. Fuel just needs to last long enough to engage your target. Fighters are usually a good choice here, since they can be built cheaply, in bulk.
2) Missile spam. If going against the AI has taught me anything, it's that very fast size one missiles that do even just a single point of damage can sandpaper down even the strongest armor. Tiny fast missiles are favored here over actual ASMs because you're looking to fire as many as possible, all at once, hopefully to poke your target full of (tiny) holes.
3) STOs. Turtle up! As ground units, STOs have the advantage over your mobile fleets in that they can dig into the planet to protect themselves. Depending on the terrain of the planet and if you have any construction vehicles around, they can be extremely hard to dislodge and destroy. Note: Only works if your STOs outrange the enemy, since otherwise they'll just sit at the edge of their range and plink you to death.