Irsay was arrested for allegedly operating a vehicle while intoxicated back on March 16.
He had $29,000 (£17,160) in cash and bottles of prescription drugs in his vehicle at the time of the arrest, and he now faces four felony counts of possession of a controlled substance.
When questioned on the incident this week, Goodell told reporters: "There have been no charges. So the answer is, until we have more information or more facts, we will let it play out."
However, Clark has hit out at Goodell's explanation, stating that the NFL chief favours team owners over players.
Clark told ESPN: "Right now, Jim Irsay is going to represent this league, represent the Indianapolis Colts, going to be on TV at the owners meetings, trying to bring a Super Bowl to Indianapolis after what he's done.
"It shows the hypocrisy of the NFL and also Roger Goodell in the way that he deals with players and the way he deals for the people he works for."
Despite not being charged with a crime, Goodell suspended Roethlisberger after he was arrested in an incident involving a 20-year-old college student who accused him of sexually assaulting her.
His initial six-game ban for violating the league's personal conduct policy was eventually reduced to four.
"When has having enough information been what Roger Goodell waits for to make these decisions? When does a charge necessarily warrant the penalty? We've seen in so many cases, Roger Goodell be judge and jury when it comes to players.
"With Irsay, what more information do we need than these aren't your prescription pills? You're obviously under the influence. You have $29k on you. There would be no questions asked if this was a player."
Irsay declined to speak about the arrest when he attended the NFL owners meetings in Atlanta on Monday.