Banner County officials are deeply unhappy with the refereeing of James McGrath and McDonagh also wants officials to check protocols in place before and after half-time.
The chairman has also insisted Clare will answer any questions from Croke Park, amid claims McGrath may have been accosted at the break.
McDonagh said: “We just want to make sure what happened in Thurles yesterday never happens again.”
He added: “We were beaten by a better team — we have no problem with that but there are issues during that match that should be analysed by the higher authorities in Croke Park. And action should be taken.”
McGrath came under fire from Clare after the first-half free count favoured Cork 12-5. That allowed Patrick Horgan to profit from placed balls and the Cork forward had posted 1-8 from placed balls before the interval.
Members of the Clare camp made their feelings known to McGrath before he was escorted down the tunnel at half-time. After the interval, the referee appeared to be waiting for Clare manager Davy Fitzgerald, who delayed his return to the dugout.
McDonagh added: “The whole match should be analysed from A-Z. They’re (Croke Park officials) big enough men to see exactly what went on there. What I’m looking for is a complete analysis of the game by GAA management. They should get this done and a report should be sent out to each of the counties.
“Everybody deserves to know exactly what went on there. We’re training county teams for a long, long time. We put a lot of effort into it and the bottom line is that I’m looking for a fair analysis of the game.”
McDonagh added: “It costs hundreds of thousands to prepare a team. I’m not pointing my finger at anybody and I want a report back from the management committee. It’s not a major thing to do.”
It is believed Clare are specifically requesting Croke Park’s views on McGrath’s officiating and incidents before and after half-time. Asked if Clare were aware of allegations McGrath was struck by a water bottle, McDonagh responded: “Let it be analysed.”