I don't want to cause problems for my friend, nor to have our friendship unduly influence the recruiting process. I have not yet spoken to my friend about it because doing so would certainly result in the latter outcome.
Of course it will. But that's not in and of itself a problem.1 You know this person well enough to consider him a friend so it would be very strange not to give him a heads-up, especially because he's actually the owner and it's a small business. Just tell him that you saw the ad and think that you could potentially be a good candidate, even if you aren't a perfect match experience-wise. Just be direct, honest and make it easy for him to say no. There are legitimate reasons not to hire friends, even if there are a few levels between you, your friend might simply prefer not to mix business with personal relationships, or they may as you suspect prefer a more experienced profile.
You could say something like this:
I noticed your company posted a position as [X] which interested me for [reasons you'd want the job]. I think my experience at [past jobs] doing [stuff] means that I'd be well suited for the role, though I realise that I don't have the level of experience [you / the hiring manager / the company] may be looking for. But I wanted to talk this over with you first in case you didn't feel comfortable hiring a friend or know that I don't have the experience [hiring manager is / they are] looking for. Of course I don't expect any preferential treatment, but I did want to check with you whether it makes sense for me to apply or not.
Of course this would sound a bit formal when among friends but you want to approach this conversation in a more professional tone than you would normally. If he seems open to the idea after you broach the topic, make it clear that there'd be no hard feelings if the company's management decides that you're not the right person for the role.
1 - Edit to clarify: what you absolutely want to avoid as a candidate is giving the impression that you're trying to use personal relationships to bypass a company's hiring process. That's definitely Not A Good Thing. But the fact that you know people at a company will of course have an impact as those people can presumably speak to your work and give references that the hiring manager or HR can trust more than those from former managers of yours that they don't know. This can just as well cause you to lose the job: if someone there knows you're a great employee but also knows that you, for example, hate project management and they know that the job they're hiring for will include a lot of that. But that's not a bad thing! In most cases your goal should not be to find employment at all costs but to find a job that you'll excel at and that perhaps don't love, but at least not hate.