Everton manager Roberto Martinez and his Carlisle United counterpart Keith Curle have both spoken out , condemning the alleged racist remarks from sections of the home crowd towards Everton's players after Arouna Kone scored the opening goal in the second minute of the game.
Immediately after the goal, an announcement was made on the public address system at Brunton Park that racist and or abusive language would not be tolerated at the ground.
"What happened is when we scored the goal, Arouna Kone and Steven Pienaar were celebrating.
"A very, very small minority in the back of the stand behind the goal made some racial remarks. As you know, there is no sort of room for that type of behaviour.
"But I must stress it was a very small minority. I want to believe that it was just an emotional reaction to the disappointment of conceding a goal."
"I thought the way the referee handled it and the whole ground handled it, they stopped at that moment.
"It wasn't an exercise of using the game to be abuse racially any of the players. It was handled in the right manner, even though you should never see incidents like that. It was an emotional reaction to us scoring a goal and it was handled very well by Lee Mason."
Regarding Kone and Pienaar, he said:
"They are ok. They were sensitive at that point and they were hurt at that moment. They were fearful at that point that it was going to develop into a difficult afternoon.
"But it was a one-off incident. The crowd itself stopped that little minority to behave in that manner.
"We will help the police and we will help Carlisle and we will help everyone to make sure that it doesn't happen again, not just in football but in life general.
"I thought the way we handled it, the referee and the announcement was a real sign of respect and it stopped the wrong doing."
Carlisle manager Keith Curle agreed with Martinez.
"The referee came over after the first goal and said some comments were made.
"One of their players heard some comments and spoke to the referee. He got a message to the fourth official and an announcement was made that it's not tolerated at this football club.
"I was made aware of it and made the relevant announcement. It is not what we want inside Brunton Park.
"The club will make all efforts necessary to find out what has happened. The club will do everything it can to identify them and the relevant punishments will be endeared to."
A club spokesman confirmed that the alleged incident was supposed to have come from the Warwick Road end of the ground, the main terrace for home fans.
"We will have our normal full post-match procedure and check video evidence to see what happened, if something happened.
"If we find out something did happen, we will deal with it to the full letter of the law."
Meanwhile, the regional Cumbria Constabulary confirmed they are in the process of investigating allegations of racist behaviour directed towards football players in today's FA Cup fourth round tie between Carlisle United and Everton.
Superintendent Justin Bibby said:
"We are investigating allegations of racist behaviour directed towards Everton players following the first goal.
"Hate crime will not be tolerated in this county and any allegation will be fully investigated.
"We ask that anyone with information makes contact with police."
Carlisle United had recently appealed to all the twenty Premier League clubs for help to rebuild Brunton Park after Storm Desmond decimated Cumbria in early December, with only Everton and Sunderland answering the call to raise money.