Existing Google Analytics events and Google Tag Manager
http://www.lunametrics.com/blog/2015/01/21/gtm-existing-tracking/
In your GTM pageview tag, navigate to More Settings > Advanced Configuration. Check the “Tracker Name” checkbox, but leave the field blank.
There is a way - you can rename the ga function in the tag manager (advanced configuration, global function name), e.g. to "real_ga" . Then you create a custom ga function in your own page that takes the parameters from your event tracking calls and passes them to the real_ga-function (so you need to change the tracker name only in one place), or better pushes them to the dataLayer (and then you can use the dataLayer values for event tracking in GTM).
But why would you want to do that ? You do not actually have a problem, your simply feel bad about your workaround. The proper answer to this is, as long as it works don't feel bad.
I had the similar configuration (Universal Analytics tag in Google Tag Manager) and I wanted to fire events from button on click.
I used petriq's comments to solve my problem and therefore want to add my notes.
Universal Analytics default event code is in this format:
ga("send", "event", ...);
You can fire Universal Analytics events from your code with the tracker name:
ga("gtmXXXXXXXXXX.send", "event", ...);
However the tracker name changes in every gtm load so I changed the code like this:
var trackerName = ga.getAll()[0].get('name');
ga(trackerName + '.send', 'event', { eventCategory: 'category1', eventAction: 'action1', eventValue: 0 });