it's a better to display your test results in Jenkins instead of creating issues for them automatically. You didn't mention what technology you’re using (nodejs, java, ...), but typically you let your test runner generate a test results file that jenkins can interprete, so it will display the results nicely. There are various jenkins plugins that can help with that.
If you want to go a step further and still create issues automatically, you can script that in a separate step of your jenkins job, using the JIRA REST API and a scripting language of your choice. It just comes down to parsing the results file and let your script create issues for the failures.