A mishap is not a career ender, but how you handle it can be. It's a learning experience.
I was approached by an individual who wrecked an airplane on his initial flight with a new operator. He hadn't been hired yet. He was interviewing for a glider tow position, did a tow to demonstrate, and turfed the airplane on landing with a groundloop that tore off a wing. When he interviewed with me, he said that he didn't feel it should count, because "I wasn't being paid yet." I pointed out that he destroyed the man's business, a single-airplane tow business, but the applicant didn't care. He handled it badly.
Show that you know what went wrong, that you learned from it, and that you handled it well. Take responsibility for your part, throw no blame, move on.
I used to fly with a captain who may be one of the few people to lose a wing after takeoff in a multi engine sea plane, and live (no fatalities). I told him he should have put it in a book. He was flying widebody international at the time. A lot of pilots out there have had incidents, mishaps, accidents, violations, etc.
Where it can affect you is the initial screening. Every application will ask about accidents or incidents. Some employers won't give you the chance to explain yourself, as they'll move on to someone else. In those cases, there's little you can do. Keep applying, keep seeking. It's not a career ender, but it is a problem which should be taken seriously.