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."
Wenger himself insists he does not feel there is a growing agenda against him.
"I don't take it personally. I am not a conspiracy theorist. I am 30 years in this job and if I was paranoid, you would know it already. I just think that when I worked for 16 years in the country I expect a certain respect.
"You can criticise me and say I am doing a bad job, but manipulative things, when they are wrong, I don't accept."
Wenger, addressing the media in a feisty press conference ahead of Tuesday's game with Bayern Munich, accepts any claims a team humbled by Blackburn, and also dumped out of the Capital One Cup by npower League Two Bradford before Christmas, cannot yet be heralded as potential kings of Europe.
"If I say to you 'we will win it this season' you will laugh at me because we just lost against Blackburn, but it can happen. Unfortunately in football, it is less predictable than that," he said.
"In Europe, we have beaten everybody, which is what people forget, and also we are the only team that has gone into a (Champions League) final without conceding a goal.
"Chelsea last season is a good inspiration for us, to show the same resilience and hope, because sometimes the luck goes your way when you have that resilience."