Does “I shouldn't have let you do it.” “shouldn't have + past participle” or “shouldn't + present perfect”

In the movie "Frame", 1947, Glen Ford, in one dialog there is:

"I shouldn't have let you do it."

Does "I shouldn't have let you do it." grammatically means:

shouldn't have + past participle or

shouldn't + present perfect?

I ask it because always after modal verbs go infinitive of verb without "to".

Does the verb "have" in that sentence infinitive without "to" of verbs "have", or it is "have" of present perfect "have let".

I'm waiting for an answer here:
https://ell.stackexchange.com/questions/205918/does-i-shouldnt-have-let-you-do-it-shouldnt-have-past-participle-or-sh