Brown appeared to react to the crowd as he made his way out onto the pitch for the second half at Holker Street with King alleging the 31-year-old defender had been the subject of racist abuse.
King: "He got called a monkey by some of the fans behind the goal. He said to the ref 'he's called me a monkey' and that's not acceptable. It's disappointing for me that we've got monkey chants and all that."
King added: "I heard it when I was coming out with Nat Brown. It seems to be happening everywhere. It's up to Browny - he said leave it but the ref [David Webb] wants to report it because it's not acceptable. We're in 2012 - what's all that about?"
Earlier, Barrow's Richie Baker had levelled Kieran Charnock's opener to force the two sides into a replay on December 29 for the right to play Cardiff.
King added: "We defended well and coped with everything in the box. I'm pleased to get the replay - they're at home and were always going to put us under pressure.
"We tried to hit them on the break at the end and we soaked up a lot of pressure. It was a tough night - first ball, second ball, smash. They played no football - that's their limitations and what they've got."
Barrow assistant manager Ashley Hoskin said: "It was actually their manager who came over and said someone had shouted something at one of their players. If that's the case, it's not acceptable. It's not acceptable in any walk of life, never mind football, and it's very disappointing if that's happened.
"I know for sure the club would take a stance on anyone shouting what was allegedly shouted.
"We're disappointed - for the first time the lads have put a proper shift in. They've shown they can defend. We saw the back four defend as a unit and we got in their faces but we knew we had to do because if you let them play they're a decent outfit."