The supporters in question allegedly hurled objects and abuse at Burnley fans and were among the 1,500 people who invaded the pitch at St Mary's Stadium following the 2-2 draw which confirmed Saints' relegation to League One.
The police are investigating incidents of disorder and have released photos of the 11 individuals who were caught on camera and Match Commander Chief Supt Matthew Greening said: "We are committed to identifying and bringing to justice those people who were responsible for violence and disorder.
"Our enquiry is aimed at sending a strong message to Southampton fans that we will not tolerate violence or threatening behaviour of any kind at football matches and we will act if supporters break the law.
"I understand it was a tough session for Saints supporters but the behaviour of a few "so-called" fans immediately after the Burnley match was totally unacceptable and there is no place for it at St Mary's or any venue in the city."
Southampton's head of operations, Brendan McGlinchey added: "Southampton FC views these incidents very seriously and fully supports the police in this initiative. The club expects to issue a number of banning orders to those identified by the police during the course of their investigations."