He said a repetition of the events, which involved mainly Rangers and Celtic and their fans but also other clubs, would be a “disaster for our national game”.
The First Minister said decent supporters, advertisers and sponsors would find it increasingly difficult to be associated with the game if such behaviour was seen in the coming season.
They would be driven away by conduct “which is not seen as acceptable in this modern age”.
Mr Salmond was speaking at the publication of 40 recommendations by the Joint Action Group (JAG) of Government, police, Old Firm, SFA and SPL officials set up after a touchline row between Celtic manager Neil Lennon and Rangers then assistant manager Ally McCoist.
The main recommendation is a National Football Policing Unit, backed by £1.8 million of taxpayers’ cash, to co-ordinate football intelligence and support post-match investigations.
Chief Constable Stephen House, whose call for a summit meeting following the clash between Lennon and McCoist led to the formation of the action group, said it would be led by Superintendent David Brown of Strathclyde Police with up to nine other officers from other forces plus support staff.
Mr House said the unit would allow a full-time focus on policing football.
Both Celtic and Rangers were at yesterday’s meeting of the JAG but neither club was represented at the press conference which followed. Their absence was explained by Mr Salmond, who said the recommendations applied to all football clubs and their supporters.
SFA chief executive Stewart Regan said it was “essential we don’t see the sort of scenes we saw last season”.
“If we are going to attract commercial partners and families into the game then we cannot allow the behaviour at some of our higher-profile games to bring the game itself into disrepute.”
Mr Salmond added: “We need to do considerable work in terms of presenting football as a positive force in Scotland.”
Tougher sentences for football-related violence are expected to be passed by the Scottish Parliament by the end of the year.