Photographs on Twitter showed winger Justin Carney and centre Junior S'au involved in apparently heated exchanges with some of the travelling fans.
There was no explanation offered from Salford at the post-match press conference, but on their official Twitter account they said: " We'd like to apologise for the behaviour of some of our fans today. We'll be working with @Giantsrl to find those involved. We do not condone any behaviour of the sort."
Press Association Sport contacted Salford, the Rugby Football League and West Yorkshire Police for further comment.