The Tannadice Park fixture was postponed at 12:15pm on Saturday due to heavy overnight rain but Hearts managing director David Southern was unhappy with the way it was handled.
"We'll be writing to the SPL to outline our concerns and to understand the process involved in this postponement," he said.
"Our concern centres around the fact that the weather in Dundee was extremely poor overnight and that the decision to call the game off came as no surprise. We would have welcomed a much earlier decision to try and avoid this outcome."
However, referee O'Reilly said he was simply acting under instructions from the Scottish Football Association and could not have made the decision any earlier.
"As far as I'm concerned, the SFA contacted me just after 10.15am on the instructions of the club, who decided that they needed an inspection," he said.
"They decided it was wise to bring in the match referee and obviously I'm travelling up from Glasgow and that was the earliest I could have got there and called the game off.
"The primary concern for the ref is safety of the players. It would have been dangerous. The forecast was that the rain was on until at least 6pm."