The Whites striker struck with an injury-time overhead kick to earn the club their first point of the season on Tuesday night.
Wood had been coming under pressure from some Whites supporters after failing to make a decisive impact in either of the club's first two league games of the season as they suffered back-to-back defeats.
However, the New Zealander finished as the club's top scorer last season with 13 strikes in 36 Championship appearanes, and his injury-time equaliser from an overhead kick against Fulham on Tuesday was his second goal in four games to start the current campaign.
Cooper was pleased to see Wood's efforts rewarded with the fine strike, and insisted that the 24-year-old is not bothered by criticism as he knows he will score if supplied with the chances.
The defender told BBC Radio Leeds: "He's come under a bit of stick has Woody but fair play to him. We've seen him bang them in every day, overhead kicks and good finishes, so we know what he's capable of.
"He'll tell you himself, as long as he's getting chances he won't be bothered because he knows he's going to stick them in."
Wood has played the full 90 minutes of three of Leeds' four matches in all competitions so far this term, but was substituted after an hour of the home defeat to Birmingham City on Saturday after an ineffectual performance.
However, he looks set to continue as Monk's first-choice partner for summer signing Marcus Antonsson, and Whites supporters will be hoping that his spectacular strike will prove to be the catalyst for his season.