But SFA president Campbell Ogilvie issued a stern warning to both Glasgow clubs for wasting the governing body's time over the incident.
Rangers took offence at comments from Lawwell regarding the Ibrox club defiantly insisting their history remained unbroken despite the original company going into liquidation last year.
In response to a Celtic shareholder who asked why authorities were still referring to their rivals as Rangers, Lawwell said: "Rory Bremner can pretend to be Tony Blair".
Lawwell quickly played down his comment as a joke, but Rangers lodged an official complaint with SFA compliance officer Vincent Lunny.
In a statement, Ogilvie said: "This week, the Scottish FA's compliance officer has reviewed comments made by the Celtic chief executive, Peter Lawwell, at the club's annual general meeting, after receiving an official letter of complaint from Rangers Football Club.
"The compliance officer has informed both clubs that there is no actionable breach of the rules. None the less, I am compelled to convey my disappointment that we find ourselves in this position, as a result of an apparent erosion of mutual respect between two of our oldest rivals.
"At a time when Scottish football faces challenges on many fronts, it is incumbent on our biggest clubs to set the highest standards.
"In this regard both the comments made, and the subsequent time, effort and resource imposed on our compliance officer to deal with the complaint, were wholly unnecessary."
Earlier, Celtic manager Neil Lennon described the row as a "storm in a tea cup".
"It was a throwaway remark," Lennon added. "I don't know what he meant by it, you will need to ask Peter.
"You have to be so PC these days, regarding a lot of topics.
"I know from my own experience, I have said a few things in the past and suffered from it, if you want to put it that way.
"It is a hoo-ha over nothing."