I was an Interview Capt for a 121 airline before and let me tell you from experience you are fine. Yes this will be on your PRIA for the next 5 years but it is not the end of your life. When I interviewed I would always ask the question about failures on Check Rides(No one does PRIA checks until you are hired to expensive). If you busted your CFI, I did think much about it because most people do the first time. If you busted a training event I would listen to make sure you took responsibility for your mistakes, with out spending 30 mins telling me the whole story, and that you learned something from the bust and have fixed the issues. Now if you made excuses, tried to place blame on the other pilot, or have multiple failures in the same aircraft we had issues.
Just be honest and make your explanation simple, We had a lack of CRM, It was just one of those days I was off my game, etc then conclude with you were retrained and passed with flying colors and since then you pay extra attention to things so that does not happen online then you will see all the interview board smiling and nodding their heads. Remember the 3 main things I would look at could I handle doing a trip with you,
can you be trained( 1 bust does not disqualify you from this), finally how do you handle change.
Good Luck!