How to ask whether you left A in B
Usually you say 1. 我钱包拉/丢/忘（在）出租车里了 or 2.我把钱包拉/丢/忘（在）出租车里了。

In 1, '我钱包' equals to '我的钱包'('My wallet') which is the subject and the verb is in passive but'被'is omitted. The grammatical expression could be 我钱包被拉/丢/忘（在）出租车里了，but no one would say out '被'here.

In 2, you use '把' as @wuyefeibao suggested and 我 is the subject, the verb being used in active voice.
In both cases, the preposition 在 may be omitted, indicating the urgent situation when you're anxious and depressed so you have no mood to speak out every function word.

Regarding your own translations 1. 丢了我钱包在出租车里 and 2. 留了我的钱包在出租车里 3. 忘了我的钱包在出租车里 are not target-like expressions. In translation 2, 留 is not the same as 忘，丢, implying you intentionally left the bag in the car (because you didn't want to carry it with you, or you wanted to give it a gift to the driver, lol?).