Anti-racism charity Kick It Out says it is "appalled" after four alleged incidents of racist abuse during the opening weekend of the EFL season.
Southend United striker Theo Robinson claims he was targeted at Saturday's League One game with Coventry City.
Stoke's James McClean, Barnsley's Bambo Diaby and the sister of Fulham's Cyrus Christie were also victims of "unacceptable discriminatory abuse".
Kick It Out says the Football Association and police have been told.
Jamaica forward Robinson, 30, says he was abused "in front of family, friends and their kids" at St Andrew's, the first match Coventry have played in their ground-sharing arrangement with Birmingham City.
BBC Sport have approached West Midlands Police and Southend United for a comment about the allegations.
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"On the first weekend of the season, these incidents should be a reminder for everyone in football that racism and discrimination cannot be ignored," added the statement from Kick It Out.
"Clubs and the football authorities must be relentless in calling out this disgraceful behaviour, and be prepared to issue strong sanctions and education sessions to any supporter involved.
"Discrimination casts a shadow over football in this country, and we will not stop highlighting the problem while it remains rife in the game."
Christie alleges that his sister was hit and racially abused by fans during Saturday's 1-0 defeat at Barnsley, while the home side's Senegalese centre-back Diaby was also the subject of racist chants.
Christie has previously condemned racist abuse he has suffered on social media.
Stoke's Republic of Ireland midfielder McClean, who has been subjected to sectarian abuse in the past, was targeted at the Potters' home game against QPR.