Years of experience is usually a loose requirement, especially if you can otherwise make up for it (with a strong portfolio, for example). Actually, most requirements are usually loose - it's not about meeting them to the letter, it's about being roughly around there.
So, assuming a position specifies a number of years of experience a bit above what you currently have, don't think twice about applying for it. However, I wouldn't quite expect you'd have much luck with a position that requires many years more than you have (e.g. 5+ years, where you only have 1).
With that said, some employers are way more strict on their requirements - they won't consider you at all if you don't meet all of them to the letter.
And years of experience could be referring to either skill (which you probably have with a strong portfolio) or seniority (to mentor or otherwise help junior employees, which you probably don't have so much of without much work experience, or at least you probably can't show it on your resume, unless you held seniority positions at school or university, e.g. been a prefect or been a captain of a team, but that doesn't have quite the same effect on a resume) - unfortunately there isn't really a way to know which one they're looking for, with the exception of being able to derive this information from the rest of the job specification.
However, the worst that can happen in applying for such a position is not getting it, right? Well, at least considering probable things happening.
With all that said, keep in mind to focus your search on what matches your level of experience. A fair amount of time should go into researching the company, writing a good cover letter, customizing your resume, etc., that you don't want to spend all this time on a position you're not even particularly likely to get (although a lot can be said for really, really wanting it) when you could've been spending it on applying for a more appropriate role (or even on improving your portfolio).