For cash donations of less than $250, the IRS lets you use a bank record, such as a canceled check, a bank or credit union statement, or a credit card statement, in lieu of a receipt. Additionally, for cash contributions of $250 or more, you will need an acknowledgment from the qualified charity.
For non-cash contributions, things become a bit more complicated and the paperwork depends on the amount and type of the charitable deduction. For example, donations of less than $250 require a receipt unless it is impractical to get one, for example if you made donations at the charity's unattended drop site. You are still required to keep reliable written records for each item of contributed property. For more information, see Records to Keep in IRS Pub 526, Charitable
Contributions.
The tax law is clear that you must have receipts to be allowed to take the deduction.
It is your responsibility to prove the amount of your donations. And as @LindaA stated above you must have proof of the cash donations. If you give cash, check or charge payments on one day to one organization of $250 or more, you must have a receipt in your hands before filing your tax return. If not, you are not entitled to the deduction.
See Records to Keep in IRS Pub 526, Charitable Contributions.