An SPL statement said Wednesday's match was called off due to "approach roads to the stadium being declared unsafe by the police".
However, the Hoops believe the Ayrshire club neglected their responsibility to "ensure the stadium locality is safe".
Lawwell told Celtic's official website: "Clearly, we are extremely disappointed that the match has been postponed.
"We have been told that the pitch is perfectly playable, but we have also been informed that the match cannot proceed due to the stadium footprint (area surrounding the stadium) not being cleared.
"Naturally this is very frustrating for the club and its supporters.
"As is always the case, it is the responsibility of home clubs to ensure that their own footprint or locality is safe and obviously in this case, this has not been achieved."