There is a term used in Jewish Law, called תשלומים. This refers to being able to make up for a missed opportunity in Halacha. An example of תשלומים that is relevant today, applies to prayers. If for some reason, someone neglected to pray one of the services of the day, he could make it up during the next service.
For example if one went to sleep without praying the evening service, Arvit, he makes it up by saying two Shmone Esreys, in the Shacharit service.
There was also תשלומים in the Beit Hamikdash. There were certain holiday sacrifices that needed to be offered on Yom Tov, such as the עולת ראיה and חגיגה. The days of Chol Hamoed, were the make up days for that missed opportunity.
In the case of Shavuot, there was no חול מועד. However, six days following this holiday were granted as תשלומים for late sacrifices. This is why we do not say the תחנון prayer for six days following Shavuot.
It certainly is important to know that there are opportunities to fix mistakes made, or missed opportunities. One must not despair if he made a mistake. There is usually a way to make things right.