Hamill was sent off following a challenge with Sam Hutchinson although the referee had appeared initially to have dismissed the Owls midfielder instead.
Heckingbottom and Wednesday assistant Lee Bullen were then sent to the stands following a touchline altercation, which could see them both charged by the FA.
The Barnsley head coach said last night that he had not seen the red card incident.
Heckingbottom said. "My frustration is I saw the referee give Sam (Hutchinson) a red card and I obviously didn’t know Adam had been sent off as well.
“I didn’t realise until I got upstairs when I thought ‘hold on, Wednesday have still got 11 players on the pitch,’ but I know I saw him give a red card. I thought they’d both been sent off.
“You can’t afford them, forget the result, that will be a player we’re missing for three games, obviously if it’s not worth appealing.
“We don’t carry a big squad as it is, we don’t want players missing games.
“I think me and Bully will both end up suffering but it’s just mismanagement. I’m going to ask him what the rules are in the technical area.
“You don’t mind their staff being up during the game if the fourth official is going to let them do that, but when you turn around after an incident and see the fourth official on your technical area and you’re trying to get them out, there’s only one way it’s going to end.”
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