Hartlepool United manager Craig Hignett and Dover Athletic counterpart Andy Hessenthaler said they discussed taking their players off the pitch after allegations of racial abuse.
Visitors Dover won 2-0, but the National League game was marred by abuse targeted at an Athletic player.
“I wanted to come off the pitch, and Craig agreed,” Hessenthaler said.
“But the players didn’t want to do that, the players wanted to stay on the pitch and they wanted to carry on.”
Hignett added to BBC Radio Tees: “I said to Andy, if that’s what you feel you want to do, then I’m behind you.”
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Tempers rose among home supporters after Dover’s Inih Effiong scored a controversial 36th-minute penalty.
The forward was allegedly abused by a small minority of supporters, with stewards and players from both sides reacting to the incident which saw the game stopped for more than 10 minutes.
Hartlepool had two players sent off late in the second half and a home fan tried to get to the referee after invading the pitch following a number of contentious decisions.
“I can honestly say that I have never witnessed a game of football like that, but it is important that we separate our reaction to the game, and the officials, to the events following Dover’s first goal,” Hartlepool chief executive Mark Maguire said in a statement.
“Whatever the rights and wrongs of the decision, or the aftermath to the penalty which was scored, Hartlepool United utterly condemn racist behaviour of any description.
“As I understand it, in this, the early stages after the event, individuals have been identified and will be dealt with in the strongest possible manner by both the club and police.”
Maguire added that he had offered an apology to Dover’s chairman Jim Parmenter.
‘You are the poison and not what the club represents’
It is the latest claim of racial abuse at football in England this season – anti-racism charity Kick It Out reported four incidents on the opening weekend of the campaign, while players such as Manchester United’s Paul Pogba and Derby County forward Duane Holmes have been allegedly targeted online.
On Thursday former England forward Peter Beardsley was suspended from all football-related activity for 32 weeks for making racist comments to players while working as a coach at Newcastle United.
Hignett said any Pools supporters identified would be dealt with “in the strongest possible way” if the allegations were proven.
“If a lifetime ban is the strongest possible way then that’s what we’ll do,” added Hignett. “We have to identify everyone who was involved in it and if that’s been proven we’ve got to sort them out.
“This club isn’t like that, we’ve got a black owner, we’re an inclusive club, we’ve got black players.
“It’s got no place not just in football. It’s a big thing in football at the moment, but in society itself. It’s ridiculous to think we’re still talking about it in 2019.”
Pools midfielder Gavan Holohan added on Twitter: “To the 99% of fans that come support us week in, week out home and away thanks for your support – you are the lifeblood of the club.
“To the 1% who racially abused a player you are the poison and not what the club represents. No place for it in society never mind football.”