Wenger and Samir Nasri have both been charged by UEFA following their protests to referee Massimo Busacca after he sent off Robin van Persie in Arsenal's 3-1 last 16 second leg defeat at the Nou Camp on Tuesday.
But Wenger continued the spat when he branded the European game's governing body as "arrogant" and a "dictatorship" in a press conference on Thursday.
However, Hill-Wood wants the matter ended because he believes Wenger will struggle to get UEFA to listen to his complaints.
"Emotions were running very high," he said in the Daily Star. "It is understandable, but I don't think you achieve a great deal by dealing with things in this way, rather than in a more private way.
"They (UEFA) are difficult people to deal with - they don't listen to you and they never have done.
"Maybe one day they might - but I am not going to hold my breath.
"I don't believe in criticising referees myself because I don't think you achieve much.
"But managers take a different view - not only our own, but also others, including one we all know about right now (probably alluding to Manchester United manager Sir Alex Ferguson). I think Arsene is very upset."
Arsenal chairman tells Wenger to cool UEFA spat
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