As mentioned in @gershongold 's link, the Rema (Orach Chaim 239: 2) writes:
וְיִקְרָא קְרִיאַת שְׁמַע סָמוּךְ לְמִטָּתוֹ, וְאֵין אוֹכְלִים וְשׁוֹתִים וְלֹא מְדַבְּרִים אַחַר קְרִיאַת שְׁמַע שֶׁעַל מִטָּתוֹ, אֶלָּא יִישַׁן מִיָּד
That is, after reciting kriyat shma in bed one doesn't eat, drink, or speak, but rather sleeps immediately.
Also cited are the Beit Yosef citing the Kol Bo who writes the same, and the Rokeach who shared this view.
It should be noted that they are addressing speaking after the nocturnal kriyat Sh'ma; not after HaMapil. Magen Avraham (239:2), however, does write that breaking after HaMapil is a problem.
However,also cited is the view of the Aruch Hashulchan, that there is no prohibition whatsoever in making a hefsek (separation) between the blessing of HaMapil, and falling asleep.