By three things the wise person may be known. What three? He sees a shortcoming as it is. When he sees it, he tries to correct it. And when another acknowledges a shortcoming, the wise one forgive it as he should.
Anguttara Nikaya I - 103

To do our best' means that at all times in our everyday life we should probe our minds so that we don't feel guilty about our mistakes, even though others don't know about them. If we do that, we are truly doing our best.