An After action report will show up after a battle has taken place telling you how many and what type of troops, of both sides, were knocked unconscious or killed. After a battle has taken place, and you end up losing all of your troops, you are then taken prisoner, to be released awhile later with some items taken, and without your party. Soldiers knocked unconscious can be taken prisoner if you win the battle.
along with the troops (if any) who were knocked unconscious. You can also let the nobles go, netting you honor and probably a relationship bonus (some lords don't like being released). If you chose to keep them, you lose relationship, but later have a chance to ransom the captured noble back to the opposing faction, giving you 1,000-6,000 denars for a vassal and 9,000-18,000 denars for a king.
If you fought the battle with an ally, after the battle, your ally may or may not speak to you. If they do, and you have a positive relationship with them, they will usually say how they were glad you came and your relationship score with them will be raised. If you have a negative relationship with them, there will likely be no relationship change, and they may insult you or tell you that your help was not needed.