Face the future, don't fix the past

From time to time one of my bosses or colleagues will point out that I have made (or presided over) a mistake. I have discovered that I have a not-always-healthy response to such a discovery--I try to fix the past before (or rather than) facing up to the future which includes the error.
Of course fixing mistakes is not a bad thing in itself, especially when it can be done easily and when the fault for the error lies entirely with me.  But when the error comes out of a process that is appropriate, fair, and agreed upon, an effort to fix the past implies not just that an error has happened, but that the process and by extension the people involved in the process, have some failing.  This may or may not be true, but it is hardly a good thing to imply.
I read a book a few years ago called Turn Towards Everything.  The book ended up being a pretty abstruse discussion of Buddhist philosophy and practice, but the title has stuck with me as a way of facing up to the future.  And so I have begun to wonder what it would look like if rather than defaulting to fixing the past our (my) first step was to face the future that includes the result of the error.  It may not be so bad.  A face the future response would focus on (1) improving systems, (2) developing the skills of people, and (3) communicating more clearly--none of them bad things.  Conversely, a fix the past response would include (1) going back on an agreed-upon process, (2) implying that participants in the process were underprepared, and (3) imagining that the outcomes of all errors are (or should be) fixable.  I am certain that this last list is less desirable than the first.