<human>: Can you summarize the given text in a few sentences?

I'll try to make this brief, as I'm working through the fallout right now. I work for a fairly large Fortune 500. Project manager. I frequently work with many teams from many organizations. During a recent project, an important (but not catastrophically so) task was not completed. I had assigned a group to do it, but they let it slip through the cracks. I (wrongly) assumed that it had been completed.  
   

Fast forward to today. We discover the error that will probably cause us to lose a little face with some customers and incur some unexpected expense. My boss finds out, and is pretty upset. Mainly because our group usually gets the blame when things go awry (as the project managers). He wants me to make sure that the errors committed by the others are highlighted and that they admit them. I'm all for accountability, and have had a call with that group. They are sorry, want to fix it, but also know that to go out of their way to expose their errors causes them to lose face, as well.  
   

I, personally, would rather just fix the problem and do better next time. I kind of don't care about the political fallout. I feel like holding their feet to the fire on this would damage a relationship with that team that I've been building for years. Any ideas?
<bot>: Important project element fell through the cracks. Multiple failures, but I might get the blame. Boss wants me to make sure that others share the pain.