Motherwell have contacted the Scottish FA's Head of Refereeing John Fleming to "seek feedback" on two penalty decisions against Celtic this week.
Manager Stephen Robinson said his team felt "really hard done by" after a crucial penalty award against his side in Sunday's League Cup final defeat.
He refused to discuss the spot-kick given to Celtic two minutes from time in Wednesday's 1-1 Premiership draw.
Motherwell issued a statement on Thursday expressing their dismay.
"Many supporters have contacted the club today seeking clarity on our position regarding incidents during Wednesday night's fixture with Celtic," it said.
"Firstly, it is unfortunate yet another Motherwell match has been dominated by a debatable decision from a match official. It is a call that has left the majority of our supporters again feeling extremely frustrated.
"Whilst everyone in football accepts match officials have a challenging role, and getting everything correct is almost impossible, it is disappointing to see high profile decisions affect both Wednesday night's match and the Betfred Cup final in the way they have.
"To that end, we have made contact with the Scottish FA's Head of Refereeing to express our views and seek feedback."
As well as the controversy over the late penalty, awarded after Callum McGregor went down in the box after a challenge from Motherwell's Andy Rose, Wednesday's game was also marred by a flurry of objects apparently thrown towards Celtic players.
Celtic captain Scott Brown said on Thursday that players need more protection before someone is injured by a coin thrown by a fan.
Motherwell's statement added: "As we do at every match at Fir Park, if any incidents are reported to us, we will fully investigate them.
"Should any evidence exist, we will take appropriate action against any individuals who have acted unacceptably.
"In addition, we will work with Celtic Football Club to fully investigate, amongst other things, the numerous acts of vandalism, including 206 broken seats, damaged toilets and graffiti in the McEwan Fraser Legal South Stand."