To some extent I feel like this depends on what kind of employer this is. A small employer where the person in the interview likely was the one who determined the offer should be handled at least somewhat differently than a large company where the offer likely came from HR (with guidance from upper management) and the folks who interviewed you likely didn't have any say in it.
For a large employer, I'd encourage you to call the recruiter back and tell them:
I'm really excited to work for your company, and I think the position is a great one. I was however looking for a salary in the range X - Y. I'd like to know if there is some wiggle room on salary before making my final offer.
That's pretty laid back negotiating, so it's unlikely to put them off, but it will find out if there is some room to go (and larger companies often leave a little room on purpose knowing you may negotiate - you don't go in with your best offer right away after all). You're not telling them you won't accept the job if they don't counter, you're just finding out if there's a slightly higher salary available. If we're talking $88k vs $85k, this can work for that; if we're talking $88k vs $75k, this probably isn't the right approach.
For a small employer, you're a bit more likely to risk the job if you counter - but you can also take more care.
Hi, I was excited to see the job offer in my inbox yesterday. I noticed you offered me $X , which is a bit below what we discussed as my desired range.
Yeah, we only had room for $X in the budget right now; I hope that isn't a problem. I tried to include some extra perks to make up for that.
Totally understandable. Any chance we could start me with three weeks' vacation time instead of two? I doubt I'd use it but it would be nice to have just in case I get sick.
Sure, that's totally doable.
Something like that - feel out for more money, if it sounds like it's not possible then see if you can get a little extra perk. Especially when you put it like that (You did offer me less than my asking price...) you're likely to get a little extra perk or two if you're reasonable. Signing bonus, money for school, extra vacation time, all of that is often easier to do than extra salary.
In either of these cases, the request isn't zero risk - but nothing is, and I think you can manage your risk carefully if you make an effort to be very polite. Don't leave yourself regretting in a year working for an otherwise great job because the salary isn't what you feel it could have been. Also don't forget that if the company really likes you and you're a good fit for the job, they don't want to risk losing you - of course this depends on how many people they likely can find for a job like yours (which you don't specify), but this isn't a one way street.