Taking responsibility

So today I was confronted about an issue at work. I hate issues at work... I have so much on my plate, it is so easy to let one slip by. The truth of the matter is there isn't enough hours in my work day to do everything. I need 8 hours + 1 of no phone calls, no interruptions. I wish I got paid for overtime. So the issue I was confronted about was a responsibility I have to make sure gets done. But the entire reason it wasn't done yet was was because someone ELSE messed up, and they kept trying to get ME to fix their problem, not wanting to do it themselves, and it had dragged on for MONTHS. It had taken too long, and had gotten to my manager's desk. I reacted in a way toward my manager that I shouldn't have - I know that. I can make excuses for the way I reacted but I'm not. I am learning to not make excuses at all but to apologize for it and immediately find a way to remedy the situation. Taking responsibility is hard for me, it's a challenge. Especially when I feel like I have too much responsibility (or more that I don't have the time I need to get what I need done done). But it all boils down to the fact that whether or not the problem was caused by me, it was/is my responsibility to fix it. So the best way to do that? Take a deep breath, and plow in.