In writing and talking about “forgiving,” I’ve often been asked about “forgiving ourselves.”
While Jewish tradition doesn’t necessarily use that particular “psychological” terminology, it’s repeatedly discussed in the context of “guilt,” “remorse,” etc.
Much Jewish teaching speaks about regretting our mistakes, but this is to motivate us to change for the better, not to depress us. Jokes about “Jewish guilt,” however humorous, don’t accurately reflect what Torah teaches.
Again and again, Judaism teaches us to be joyful, even (perhaps especially) when it comes to penitence:
“At times it is well to avoid thoughts of holiness and penitence when they come in a spirit of melancholy…When thoughts of fear and penitence occur to a person in a spirit of melancholy, let him [her] distract his [her] mind from them until his [her] mind becomes more settled… ” 
Rabbi Morris Lichtenstein likewise doesn’t speak about “forgiving ourselves,” but he does write about needless remorse in his discussion of “grief”:
“…when repentance [i.e. feelings of guilt or remorse] deepens and turns into grief, robbing of all quietude the heart in which it dwells, it ceases to serve its high function and becomes a destructive tool…” 
“We do not need to rebuke our past, or punish ourselves for it, we have only to transcend it, to live a better life in the present and aspire to an even better one in the future. When we permit repentance to bite too deeply into our soul, we are simply inviting moroseness and unhappiness in the name of atonement. We are, in reality, making atonement more distant by making ourselves miserable. Man attains the height of his [her] own perfection through joy.” 
As we look back on our lives – to the recent or distant past – do we find ourselves feeling regret, even shame? Do we say to ourselves, “If only…” about one or more things that we did or didn’t do?
We can’t change what has already happened.
But we can use it as the first building block for a positive future:
“Ask yourself, ‘Will my blaming myself help me improve or not?’ To the degree [that] self-blame motivates you to change for the better, it is positive. Self-blame that prevents improvement is counter-productive and should be overcome.” 
Of course, this isn’t meant to minimize the seriousness of what we might have done. It certainly shouldn’t be used to make light of our responsibility, as if to shrug it off with a callous declaration of “my bad.” It simply means: Sadness that prevents us from doing better is of little or no use. As Bob Dylan wrote in a different context: “…now ain’t the time for your tears.” 
Rav Kook further tells us that in practical terms, too, “penitence” or “repentance” is best focused at first on the future, not the past:
“The basis of everything is the ascent of perception, the intensification of the light of the Torah, and penitence in action is to follow closely, at first with reference to future behavior, then with matters of the past that lend themselves to easy mending.” 
Of course, it’s impossible in a short blog-post to explore this topic in the depth and breadth that it deserves. The sources cited here can make a more-than-adequate beginning to your investigation of this topic. They can also lead you to further sources.
But the teaching is clear: Personal change comes best out of joy.
Focus on your present and future before working on your past.