It seems to be a dispute in the poskim.
The position that one is obligated:
The Chazon Ish (quoted in Orchos Rabbeinu v.2 p.110, and in טעמא דקרא, הנהגות החזו״א אות י״ח) was mapkid to eat melaveh demalke on Motze Yom Tov.
The Brisker Rav was asked (פניני רבינו הגרי״ז, עמ׳ רמ״ב) if there is an obligation for melave dmalka on Motzei Yom Tov, and he responded: "אינני יודע למה לא" (I'm not sure if he meant to pasken that there is, or although the accepted halacha is that not, he doesn't understand why it should be different to Shabbos).
See also Tashbatz Katan (§82), who insinuates that there is a seuda on Motze Yom Tov:
וכשהוא מבדיל במוצאי שבת או מוצאי יו״ט על שלחנו, מכסה את הפס כמו שעושים בשב, ואמנם אינו מצריך ב׳ לחמים במוצאי שבת קדש או מוצאי יו״ט
The Position that one is not obligated: However, Shmiras Shabbos Kehilchoso (63:4) rules that there is no obligation on Motzei Yom Tov.
R' Moshe Shternbuch shlit"a (Moadim V'Zmanim v7 §153, and Teshuvos V'Hanhagos v6, §120) explains the difference between Shabbos and Yom Tov:
(a) On Shabbos there is no hekker that the Seuda lkovod shabbos, so Chazal instituted a special seuda on Motzei Shabbos. On Yom Tov, however, where there is the extra בשר ויין (as well as the מאריכין בסעודה, as per the Rambam), there was no need to institute the separate seuda.
(b) On Yom Tov, there is no neshama yeseira. (see Tosfos Beitza 33b, and Pesachim 102b).
(c) One should have hot food on Motze Shabbos (Shabbos 119b) to show that one could not heat up food on Shabbos. On Yom Tov, this does not apply.
The Leket Yosher (OCH p.58) gives testimony that his Rebbi, the Terumas Hadeshen, did not eat Melave dMalka on Motzei Yom Tov.