The Premier League visitors eventually came out on top 4-2 but only after trailing by a goal at half-time and then falling further behind just 32 seconds after the restart.
Hodgson revealed afterwards he had warned his players before the second round tie they were up against a good side, and his words proved correct.
It was only after the former England boss made a triple substitution in the 55th minute that the tie swung in Palace's favour as they netted three times in five minutes.
The 76-year-old sent on Jordan Ayew, Eberechi Eze and Jeffrey Schlupp and the transformation in the match was almost immediate as the Pilgrims were rocked by the three-goal salvo.
Hodgson said: "I didn't enjoy the first half very much. I thought they [Argyle] were very good throughout.
They are a good team and I thought they fully deserved their lead at halftime.
"I don't think we got anywhere near close enough for my liking to cause them problems and to look as though we were going to get that equalising goal.
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