illustration (attribution, if any possible, is at the end of the article)
We can all share this 'regret' of failures (at practicing the Dharma wholeheartedly, at sorting out a situation, at responding constructively to what life throws at us, etc.), but we shouldn't see it as a regret. And this is a choice we have to make.
Instead of regretting, we can rejoice at the awareness we have of our 'faults', of our 'mistakes', of our 'imperfections'… for the awareness gives us the opportunity to learn, and thus to do better from now on (whatever 'better' means in our respective circumstances)! Our path is a path of cultivation, and the awareness is the birth of taking responsibility.
We can then let go of regrets and of other narratives about the past, without forgetting the lessons. We can forget the "personal take" on the unwholesome tendencies that manifested (we can avoid the reification "I'm worthless, useless, inadequate, etc.") and cultivate wholesome tendencies anew. [Similarly, we can avoid conceit and cultivate wholesome tendencies anew, instead of thinking how great we are because we did a few good acts.]
"Forgive and forget" (gplus.wallez.name/RdCyz2fTWJG) doesn't only apply to 'others', it applies to 'all' including ourselves. Not applying it to ourselves is to 'separate' ourselves, to make us 'special', i.e. to feed the 'self'!
The lessons from failures are about causality, not about who we 'are'.
To think most or even all lessons are about causality in relation to us specifically is to be obsessed with ourselves, a clear sign of ignorance: while causality relates to a context, there's no need for aggrandisement of our importance / relevance in the said context.
Instead of regretting, instead of falling for the temptation of "stepping down" (from responsibilities we took, and in relation to which we think we failed to contribute 'enough'), we can rejoice and —via learning, via cultivating wisdom— we can "step up".
Unattributed image: daughters of Māra, attempting to distract the Buddha from his quest for a solution to unsatisfactoriness. It may be noted that the Buddha himself could have been disappointed that he didn't find the solution with his two teachers or via years of asceticism… but, instead of concluding he was a failure, he simply learnt —through experience— what works and what doesn't, and only then awakened.