Stockport County and AFC Telford United have condemned the actions of some fans after incidents at their FA Trophy semi-final second legs on Saturday.
Two supporters ran onto the pitch after AFC Fylde's winning goal against Stockport at Edgeley Park.
The Hatters say they will give lifetime bans to the fans when identified.
Meanwhile, fellow National League North club Telford say they received a number of reports of racist abuse after their defeat by Leyton Orient.
Greater Manchester Police say they are investigating the incident at Stockport while BBC Sport has also contacted the Football Association.
"We are embarrassed by the behaviour of the individuals who ran onto the pitch despite the repeated warnings we have issued advising people not to enter the field of play," a Stockport County statement said.
"We have been analysing CCTV and other footage in order to identify the two main offenders and we are continuing to liaise with Greater Manchester Police, as this is a criminal matter. We are also seeking to impose lifetime bans from Edgeley Park on these individuals."
A crowd of 6,000 attended Stockport's 3-2 defeat by Fylde, while National League leaders Leyton Orient won 2-1 at Telford for a 3-1 victory on aggregate to reach the final at Wembley on 19 May.
AFC Telford United said in a statement: "We can confirm we have also received several reports of an individual who directed racist abuse at an opposition player as well as several supporters who threw a number of objects onto the field of play above the away dugout.
"These incidents have been reported to the FA as they were picked up on the match officials report.
"As a football club, we will not tolerate behaviour which brings our name into disrepute, and we are committed to taking action wherever we have evidence. We will also share information with the Police so that criminal proceedings can be considered."
Leyton Orient confirmed that a number of objects were thrown at playing and backroom staff as well as several reports of racial abuse directed towards a member of their squad.
"We will fully support AFC Telford United and the relevant authorities with the investigation into these incidents," an Orient statement said.
Telford local policing commander, Superintendent Paul Moxley, said: "We are actively investigating the events on Saturday including a report of racist comments being directed towards a Leyton Orient player.
"Such behaviour is totally unacceptable and I would appeal directly to those in the crowd on Saturday who heard or saw this to contact Telford Police and help us take action against the offender.
"With the help of genuine fans we will be in a positive position to deal robustly with the individual concerned and work to stamp out such abhorrent behaviour."