Three flares were thrown on to the pitch at Millwall's Den on Saturday, apparently from protesting West Brom fans
The EFL has outlined its intention to tackle the growth of "unacceptable" anti-social behaviour in the game, with a threat of increased police action and a strong 'stay away' message.
This season has been marred by regular accounts of offensive chants, pitch invasions, fans throwing objects and abuse on social media.
"Any form of anti-social behaviour is unacceptable," said an EFL statement.
"Those intent on causing trouble are not welcome at our matches."
Among this weekend's main off-field issues were offensive chants by MK Dons fans at Wycombe striker Adebayo Akinfenwa, objects thrown at the assistant referee in front of Rotherham fans at Crewe, and West Bromwich Albion fans throwing smoke flares on the pitch during their 2-0 defeat by Millwall.
The statement said: "Following multiple incidents of inappropriate and reckless crowd behaviour on Saturday the EFL will work with the relevant authorities and respective clubs to ensure those responsible are held to account.
"Whilst these instances only represent a very small section of people attending matches, the mindless few who choose to behave in this way are only demonstrating a complete lack of respect for the clubs they claim to support.
"Our message is simple - those intent on causing trouble are not welcome at our matches and we ask you to 'Stay Away'.
"Anyone found to be behaving offensively at a football match can expect to be dealt with by the police and the club, who will continue to work closely with supporter groups to address the causes of violence from individual fans and will always support prosecutions when that is the appropriate course of action to take.
"The EFL is disappointed that on a day when the footballing focus was on our League competition, the discussion is once again about matters off the pitch.
"We will continue to work closely and collaboratively with our clubs, safety advisory groups and local police forces to ensure security operations in place are robust and effective, whilst also providing support when any incidents do occur."
Source: bbc.com