The Gunners manager reacted angrily to questioning about his future on Monday, as reports claimed that despite a likely eighth season without silverware he was set to agree a two-year extension.
Wenger's future remains far from clear - but Hill-Wood was quick to reiterate the club's backing of their manager.
"You have your ups and downs and we are having a bit of a down," Hill-Wood told the Daily Star."But some of the reaction has been a bit hysterical.
"You hear clubs being criticised for sacking their manager too quickly. Now there are people out there calling for us to sack a manager who has been a huge success for 15 years.
"That does not help much. I have been extremely disappointed by some of the recent results.
"I have been an Arsenal fan for a lot longer than most so I think I know what it feels like. It hurts a lot and I am sure Arsene is hurting too.
"He is very diplomatic and calm but deep down he feels very strongly and he is as upset as anyone.
"It's not just me who is backing Arsene. (Major shareholder) Stan Kroenke is very supportive too."
I don't get what people fail to understand about this situation. In roughly 2005 the board will have told Wenger; "You know that huge stadium we're building on expensive North London land?" "Yes." "Well, it's VERY expensive. To pay for it we cannot invest as much money in the team as we have been, for about 8 years." "Oh dear, you cannot expect me to challenge for the title under those conditions." "We don't expect that, it would just be very good if you could maintain a Champions League place every year, we'd be more than happy with that." "The fans won't like it." "No, but if you can pick up the League Cup or FA Cup once or twice in this period we might be able to smooth things over." "What if that doesn't happen?" "We'll still back you for as long as we finish top 4 because that would be a great achievement in this situation. Once the stadium is paid for we'll give you loads of money to get the team back to the top again."- shenkenshalken