Yes, you should write the authors.
I disagree with both @aeismail and @Kimball, in that I believe it is important to address the incorrect reference, and you should go to at least some effort to do it. Since it's not a critical reference in the paper OP mentioned, I would not do much, but we should be striving for published research to be absolutely correct on the facts (as opposed to opinions/perspectives/etc) so as not to confuse future readers.
So, a minimum of something like this (the wording is just a suggestion of course):
I've recently read your paper Their paper
. Some nice words about their paper so as not to appear too hostile
. I've also noticed the paper quotes own my work in Your paper
regarding technique X. However, that paper of mine does not actually discuss technique X nor use it. Did you intend to refer to another paper (e.g. Some other paper which might be more appropriate
)? Regardless, I'd like to ask you to consider taking some action to address this issue (perhaps by contacting The Journal
), to ensure readers are not confused by the reference.
would be in order. Be respectful in addressing them.