I would have fallen for.
This actually isn't a past tense. Here's how it works: when you use the verb "to have" as an auxiliary verb - that is, just like you did, but also when you say "I'm not hungry, I have already eaten", the verb that comes right after it will be in the PASSIVE form (or in the V3 form - some ESL teachers may use this term). Examples:
I ate - I have eaten (this is the passive form because you can say "the bone was eaten by the dog")
He came - he has come (this is tricky - present is "come", past is "came", passive is "come" again)
I went home - I had gone home
Of course, there is a difference between "I have" and "I had", but that's a different story altogether :)
Good luck!