The EFL condemned "unsavoury scenes" at the end of Millwall's 1-0 win over Bradford City when hundreds of fans burst past stewards.
A small number then taunted Bradford players as they went to the dressing rooms. Millwall manager Neil Harris ordered all supporters from the pitch and the club's players condemned the behaviour.
"The EFL will be writing to Stuart McCall and his Bradford team to apologise for the situation they found themselves in," the English Football League said in a statement.
"The EFL will also raise a number of concerns with Wembley as to how the fans were not only able to access the playing area but then able to get so close to the Bradford City team, who showed great restraint given an incredibly challenging and difficult situation," it said.
"We cannot allow a set of circumstances to exist where the playing area becomes an appropriate place for fans to celebrate and Wembley, like stadiums across the Country, have to be prepared to deal with the type of events that emerged on Saturday efficiently and effectively so as to ensure there is no repeat."
The end-of-season playoffs are particularly emotionally charged, as teams seek promotion in a one-off game at English football's national stadium.
Next Monday Reading play Huddersfield in the Championship playoff to reach the Premier League. Security will be tight for a game which is often referred to as English football's most lucrative, with at least 100 million pounds ($130.07 million) on offer to the winners.
The EFL said it had witnessed an "increased number of pitch invasions" at various grounds this season and will work with clubs and supporter groups over what "practical measures" could be taken to reduce the problem.
Millwall have a long history of crowd problems and in 2013 their supporters were criticised after some fought among themselves during the FA Cup semi-final defeat to Wigan, also at Wembley.
(Reporting by Neil Robinson; editing by Mark Heinrich)
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