Syntax error when adding links to images for template

Dead simple (I think/hope), I can’t work out how to provide a path to images inside php strings that doesn’t give me a “Parse error: syntax error,unexpected T_STRING in…”

Trying to place an icon after generated links, so for example I have:

<?php twitter_messages('atwitterid', 5, true, true, '<br />Go to Tweet', true, true, false); ?>

I need

<?php twitter_messages('atwitterid', 5, true, true, '<br />Go to <img src="<?php bloginfo('template_directory'); ?>/images/twittericon.png" title="Twitter Link" alt="Tweet" />', true, true, false); ?>

I know if it will work, the template directory path needs to be echoed, but even then I can’t find any combination that works.