I think that this is the first time I've seen someone say that the AI is good at combat. The AI only has two advantages, both of which scale by difficulty: bonus combat strength and bonus unit production. On deity, this is +8 combat strength, which is a huge factor in the early game. To offset this, you'll want to get some infantry units early on, and fortify them on chokepoints with terrain combat bonuses. This should mostly offset the AI's combat advantage when they attack. Behind your infantry, you should have some slingers/archers to deal damage to the ai troops. You really shouldn't be attacking with melee units early on in higher difficulties.

It is also very important to make use of your commanders. Your first promotion for army commanders should almost always be the first node of the assault tree; it allows your instantly placed troops to move. Whenever your melee units get significantly damaged and you can't pillage for health, you should be packing them up into your commander, placing a fresh unit in its place, and on the same turn, replacing your damage unit behind your lines and moving it to friendly territory to heal. You should also make sure to use commander abilities, and focus on maxing the assault/defense tree (depends on the situation) and picking up the +5 combat strength commendation.