No, you can’t claim a credit on this year’s return if you didn’t receive a benefit from the $10,200 exclusion on the 2020 return.
There wasn’t an actual credit against tax; it was an exclusion from income, which is a different beast, which doesn’t lower your tax directly, but lower the income on which your tax was based.
Your best bet is to check what happened with your return, as far as the exclusion is concerned. You can do this by setting up an online account with the IRS using its Your Online Account page.
This will allow you to verify the status of your returns and has information on payments, refunds, stimulus and more.
To sign up, have your photo identification ready. More information about identity verification is available on the sign-in page.