There are points to be made for each side in this question.
On the one hand, some people would argue that it is perfectly proper for a victim to be able to sue the defendant from a criminal trial even if that defendant was acquitted. The main reason for this is the fact that civil cases and criminal cases have a different standard of proof. In a criminal case, the defendant must be found guilty beyond a reasonable doubt. In a civil case, the defendant must only be found liable by a preponderance of the evidence. Therefore, these are two really different kinds of legal proceedings. If a defendant has been acquitted, it does not mean they did not commit the act they were accused of. By bringing a civil case, the victim gets some chance at justice if the defendant really did commit the crime.
However, while this is not technically double jeopardy, it certainly smacks of it. It seems like a victim who sues a defendant who just got acquitted is simply trying to have a “redo.” This does not seem at all just. It seems that someone who has been found not guilty of a crime should not have to face any other charges for that same act.
I would tend to take the latter position. It seems to me that people who sue after defendants have been acquitted are simply trying to get a second chance (unless they are trying to extract money from the defendant) at a case that they have already lost. They are trying to take advantage of the lower burden of proof to get at the defendant in some way.
Think of the O.J. case. They lost the criminal case and won the civil case, not that that did a whole lot of good.