What does one do when he finds out on Shabbos/Yom tov that he used a bag of carrots that were a product of Israel and has no hashgacha on it? Is there any way to designate teruma and maaser to take effect after Shabbos and then be mutar to eat the food? Also, is the pot that the carrots (presumably tevel) were cooked in ossur? Thank you.
No, one can not take off Teruma on Shabbos,or stipulate for after Shabbos.
Mishan Beitza 36b, SHulchan Aruch O:C 339:4
The pot is absorbed with tevel ans assur, however when you take off Teruma and Maaser from the carrots you can have in mind for the absorbed flavor in the pot as well and thereby permit it for consumption. See Tshuvos Vhanhagos 5:304:3.