The Saints objected to the language Clattenburg used in an exchange with their England midfielder Adam Lallana during last Sunday's 2-1 defeat at Everton.
And they wrote to the referees' governing body, the Professional Game Match Officials Limited (PGMOL), on New Year's Eve, outlining their concerns.
Having subsequently reviewed the incident, the PGMOL has struck out the complaint, but Southampton are not happy about the decision.
Saints not satisfied
A club statement read: "An official insulting any player, no matter his intentions, is clearly not acceptable behaviour.
"For this reason, we do not accept the verdict of the PGMOL in relation to this case, and do not consider the matter to be over.
"Under the circumstances, we do not feel it appropriate for Mr Clattenburg to officiate in any of our matches until this matter is properly resolved."
The exchange in question is believed to have occurred after Clattenburg had turned down vociferous Southampton appeals for a penalty.
The Southampton letter claims Clattenburg said to Lallana: "You are very different now, since you've played for England. You never used to be like this."
No further action
However, the PGMOL released a statement which read: "PGMOL is committed to constructive dialogue and communication with clubs, managers and players.
"On December 31, PGMOL received a letter from Southampton, who raised concerns about the conduct of Mark Clattenburg following their game with Everton on December 29.
"In a written response to Southampton, PGMOL acknowledge that their complaint has been considered in full.
"However, having reviewed the footage, and spoken to the team of officials, as well as the Premier League match delegate, it has been found that there is no case to answer.
"Mark has the full support of PGMOL Management and will be considered for selection for all and any matches going forward in the usual way."
Clattenburg on duty at derby
Clattenburg will therefore take charge, as planned, of Saturday evening's FA Cup third-round tie between Arsenal and Tottenham at the Emirates.
Last season Clattenburg was accused by Chelsea of racially abusing midfielder John Mikel Obi during a fractious match against Manchester United at Stamford Bridge.
However, an FA inquiry ruled that there was no case to answer and, six months later, he was free to officiate at Chelsea fixtures again.