Blackburn Rovers footballer Robbie Savage was confronted by a Burnley supporter during the Lancashire derby at Turf Moor on Sunday.
A supporter is held by police after confronting Robbie Savage
The supporter squared up to Savage in injury-time of the FA Cup tie before he was tackled by police.
After the match, Rovers manager Mark Hughes said: "God forbid, the guy who came on had had a knife."
A break-dancing male streaker also ran on to the pitch, while there was a coin thrown at Burnley's Jean-Louis Valois.
And at half-time, another fan broke through security and got on to the playing surface.
A 600-strong police contingent was on duty for the match, but Hughes believed fans should have been controlled better.
He said: "For three people to encroach on the field of play was careless and it should be looked at.
"Sometimes it's difficult if people are determined, but sometimes stewards and the police have to be more aware of the potential of that. They were slow to react."
The FA is likely to investigate the incidents which marred the game, while the police will be making a report.
Burnley chief executive Dave Edmundson said the club had taken every possible precaution in light of the intense rivalry between the two clubs.
He said: "It's always disappointing when things happen like they did, but if people are determined to get on the pitch then they are always likely to get through.
"You cannot legislate for everything. It's a very difficult job to ensure things do not happen."
In 2002, Blackburn's reserve goalkeeper Peter Enckelman was involved in a similar incident when playing for Aston Villa against Birmingham City.
A Birmingham fan was jailed for four months after confronting Enckelman on the pitch.