Telling your manager “I messed up” before they find it is one of the fastest ways to get trusted with more.

Managers are not mainly measuring whether you make mistakes, since everybody does and they know it. What they cannot work with is not knowing, because a hidden problem takes away their ability to plan and turns something small into a surprise. Reporting your own error proves you can be relied on to report the next one, which is the whole basis for handing anybody more responsibility.

Tell them the next one yourself, early, in one sentence, with whatever you have already done about it. Skip the long justification. Then actually do the part you said you would do.