Should I be worried and take proactive action and try to fix this mess
or just as well I could wait for statute of limitations to kick-in?
No, you should not.
If you filed your tax return reporting all this gain and paid your taxes correctly, then there wouldn't really be much penalties. But collecting these penalties is the responsibility of the agencies (the IRS and the FTB respectfully). The IRS has up to 3 years after you file your tax return to assess whatever they want to assess. the FTB has 4 years. If they don't do it - the statute of limitations kicks in.
You can always volunteer and send them money, of course. But why would you? If they ask for it - pay it. If they don't - keep it.
The case would be different if you "forgot" to report the gain or pay the taxes due, but then the agencies would almost certainly come after you. For penalties, especially so small where there's no real tax liability - they probably won't even bother.
In any case, it may be that there are no penalties at all. You may have qualified for the "safe harbor" rule:
Estimated tax safe harbor for higher income taxpayers. If your 2015
adjusted gross income was more than $150,000 ($75,000 if you are
married filing a separate return), you must pay the smaller of 90% of
your expected tax for 2016 or 110% of the tax shown on your 2015
return to avoid an estimated tax penalty.
If your income is below $150,000 then the safe harbor is 90% of current and 100% of last year.
That said, you don't really need quarterly estimates. If you're a salaried employee - just adjust your W4 accordingly and have the withholding from your salary to cover all of your tax liabilities. This way you wouldn't need to cough up more money when you file your tax returns.