I used to have a good overview for all the regulating screws of consequentialist theories, but I can't remember right now. So I'll give you some ideas without much structure.
That is not a bad criticism at all. It very much depends on the utilitarian framework in question. Firstly, you'll have to keep in mind that murder is taken as a harm. Certainly it's an indirect harm: so in most cases it will cause suffering to family, friends and so on. But it can also be taken to be a direct harm, even if the person killed doesn't feel anything (imagine painless death while sleeping). If we don't think that's the case then there are conceivable scenarios. There are more factors though. Guilt from the murderer, general changes in society, and so on.
How they get handled depends on the utilitarian framework in question. Let's look at the "aim" and the theory of value behind it first. For total utilitarianism - which looks at the resulting absolute amount of happiness - it's only an issue if and only if negative happiness is a thing. If suffering and happiness aren't taken to be a single scale or if suffering is taken to be a zero then this won't work. For average utilitarianism - which looks at the resulting average happiness - it would still be a problem unless some restrictions apply. There are more options than those, but it should've given you an idea.
Then it also depends which perspective and what object we're evaluating. So if we're agent relative or if we only look at rules instead of acts then this will change things.
Also, the direction your idea takes isn't the only one. I'd advise you to take a look at Parfit's idea of the repugnant conclusion if you're interested in more such issues.