An official report has found "insufficient evidence" of racist abuse being traded between players during a Premiership game on Saturday.
Northampton scrum-half Mark Robinson has been given a written warning after being found to have used "inappropriate language" towards Bath's Andy Higgins.
But both players, their team-mates and match officials all testified that there had been no racist remarks.
Robinson said he had become angry when Higgins would not return the ball.
Five spectators - four Bath supporters and one Northampton fan - made complaints during the match, which led to referee Wayne Barnes stopping play in the 57th minute at Franklin's Gardens on Saturday in order to speak with both captains.
"The words Mark Robinson used were entirely inappropriate and could be considered abusive and offensive"
Higgins said he had not heard any racist statement, although he admitted Robinson had "verbally had a go at me for walking off with the ball".
He added: "I did hear some of this, but what I heard was in no way racist, just the norm between players when [they] sometimes are aggrieved at a situation."
Robinson admitted to using a string of abusive swear words, which were, Blackett said, "entirely inappropriate and could be considered abusive and offensive".
Blackett added: "Although it did not affect the game or the other players it clearly incensed a small section of the crowd.
"High-profile players must be aware of the consequences of what they say and do when playing in front of large crowds or in a televised match and must be careful to control themselves."
Both clubs launched their own investigations, which they said found no evidence of racist abuse.
Northampton said they would conduct a more extensive internal investigation.
Only one previous investigation into racist abuse by players during a Premiership game has taken place.
Gloucester's Olivier Azam was cleared by an RFU panel of abusing Newcastle's Epi Taione in a game against Newcastle in December 2002.
Then Newcastle coach Rob Andrew, now the RFU's director of elite rugby, accused hooker Azam and Gloucester fans of abusing the Tongan flanker.
The case was subsequently thrown out by the panel chaired by Michael Belloff QC in January 2003.