Upvote:2
You are not going to get a stamp on your new passport, because you didn't use that passport to enter. The stamp is just a one-time record; you cannot replace it.
Usually, the thing that matters for a foreigner to be able to stay in the U.S. is the I-94, which documents their status and duration of stay. For people entering since mid-2013 by air or sea, the I-94 is electronic, and so the loss of a passport would not affect the ability to look up and print out the I-94 anyway. For people entering by land, they may still get a paper I-94, and if the paper I-94 is lost, then it is necessary to apply for a replacement I-94.
However, as a Canadian citizen visitor, you are generally not issued an I-94, even before 2013. You can head to the I-94 website to see if you have one; if you do, then that's all you need. If not, then I guess your copy of the entry stamp can serve to show that you entered legally.