But SFA president Campbell Ogilvie criticised both clubs for wasting the governing body's time.
Rangers reported Lawwell to SFA compliance officer Vincent Lunny for his cryptic comment regarding the club's assertion that their history remained unbroken following the liquidation of the original company last year.
Lawwell, responding to a Celtic shareholder who asked why the football authorities were still referring to the Ibrox club as Rangers, said: ''Rory Bremner can pretend to be Tony Blair''.
Lawwell quickly claimed his remark was a joke but Rangers did not see the funny side.
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.''
- Sports & Recreation
- Rangers Football Club