But the defender admits his sending off on the stroke of half-time was "hard to take" as referee Brett Huxtable apparently agreed he slipped.
It comes after the on-loan Sheffield United was given his marching orders in the 43rd minute after clattering into Jonson Clarke-Harris by the touchline.
Leading 1-0 at the time courtesy of Gary Madine's early strike, Pool went on to lose the game 2-1 to suffer an eighth defeat in their last 10 games.
Writing on Twitter after the game, Heneghan said: "Apologies for today, but when the ref agrees you slipped and still makes the decision it’s hard to take.
"The boys dug in deep but it was always going to be tough. I’ll take the blame.
"Keep getting behind this team as there’s one thing for sure which is the togetherness!"