Welcome to the Forum, mspaetauf!
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If you're losing 2 or 3 units to take out one defender, something is wrong. Since you didn't give any specifics (like 2 or 3 Archers to take out a Musket) I'm going to assume that you are talking about 'equal' units. Archer (2 attack) vs. Spear (2 defense), for instance. I'm going to further assume that this combat is on dry, flat land, say plains or grass and not forests, marshes, hills, etc.
If you are attacking with Regular units and the defender is Veteran, it will be bloody.
If you don't have any bombardment units (catapults, trebuchets, cannons, etc), to soften up the units you are attacking, it will bloody.
If you engage in anything like a fair fight, it will be bloody.
So....
Don't build Regular units past 3000 BC or so. Sneak in a barracks into the build order in your core cities and make Veteran units from then on. This will give your units more stamina in attacking and defending. It won't increase their attack or defense values in any way. But a Regular unit can lose 3 rounds of attacks before it dies. A Veteran can lose 4 rounds before it is dead. So what may kill a Regular unit, the Veteran will survive, then heal and live to fight another turn. The Regular unit is dead and has to be built again.
Build bombardment units in cities that lack a barracks, since these units do not get any type of Veteran status. Use them to reduce the defenders down a hit point or two, which makes them easier to kill with your other units. Even the bigger guns (artillery) sometimes miss, so have plenty (a judgement call) before you start. These units can be captured but if you are careful to defend them that won't be a problem.
Try to avoid fighting healthly units. Sometimes you must, but even then, try to make sure you have enough units to finish the job. Avoid attacking a solo unit that have nearby friends. If you kill it, your unit will advance into that tile and may have to suffer multiple counter attacks from the AI. If your unit is wounded it will probably die.
Hope this helps. If you can specifics, that will help, too.