It came after Arouna Kone fired Everton into an early lead at Brunton Park.
Aaron Lennon added the second goal and Ross Barkley fired the third.
A public address system message announced any abuse would not be tolerated, and Cumbria Police issued the same message on Twitter, asking anyone with information to report it.
Mason spoke to Martinez about the abuse aimed at Everton players.
“I thought it was dealt with in a very good manner,” Martinez told BT Sport.
After speaking to Carlisle boss Keith Curle, it was agreed there should be a warning to spectators.
“We agreed to make an announcement. I thought the referee was very good in how he dealt with that,” Martinez said.
“It was just a reaction, something that we don’t want to see.
“It was just a reaction to the celebration of the goal and that was it.
“It would be wrong to highlight such a moment in an enjoyable footballing festivity.”
Manuel Pellegrini seems set to include Kelechi Iheanacho in Manchester City’s Champions League squad, after the 19-year-old striker’s treble in the 4-0 FA Cup win at Aston Villa on Saturday.
Iheanacho was omitted from City’s Champions League squad for the group stages but with Sergio Aguero City’s only fit striker, Iheanacho is likely to replace the injured Samir Nasri ahead of Tuesday’s registration deadline.
Pellegrini said: “It’s a decision we are going to take this week, before the last date. We need him because of Bony’s injury.
“I see him working every day so I know what he can do.
“Maybe I received some criticism why we didn’t replace (Stevan) Jovetic and (Edin) Dzeko, and I answered we had Kelechi.”
Raheem Sterling finished the rout in the second half after Iheanacho’s goals, which included a first-half penalty, left Villa to focus on Barclays Premier League survival.
After the 4-1 win at Colchester, Eric Dier believes Tottenham are unburdened by pressure and enjoy being in contention for major trophies.
Nacer Chadli scored twice on his 100th Spurs appearance, while Dier and Tom Carroll were also on target in the win at League One’s bottom club.
Dier said afterwards: “I think the whole team is just really enjoying themselves at the moment.
“I don’t think we play with pressure. We enjoy ourselves, we play freely. We’re a young team.
“I think that shows. We express ourselves and hopefully we can keep doing that.”
The match was partly overshadowed by a clash of heads between Colchester team-mates Alex Wynter and Tom Eastman in the second minute.
Wynter had to go to hospital after losing consciousness in the collision, but Colchester reported later that results of a scan were normal.
Having lost a final as player and manager, Alan Pardew took Crystal Palace a step closer the cup glory it craves with a comfortable 1-0 win over tired Stoke.
“I’ve said it before: lesser teams than the quality I have have won this competition in recent years.
“We’ve got the talent to win it, you need a bit of luck with the draw: we don’t need Man City away, we don’t need Chelsea away, someone at home would be nice.
“Third-time lucky? I’m an eternal optimist.
“I’m always conscious of this competition, I’ve come so close on two occasions, that it’s a strong bond in me to try and win it.
“This team is every bit as good as that (West Ham) team I took to that final in 2006, but you do need a break here and there.”
Wilfried Zaha impressed for Palace, scoring the game’s only goal in the 17th minute.
Watford manager Quique Sanchez Flores also highlighted how prestigious the FA Cup is to his players after they advanced to the fifth round with a 1-0 win over Nottingham Forest, thanks to an 89th-minute goal from substitute Odion Ighalo.
Sanchez Flores did make seven changes to his starting line-up, but reiterated the FA Cup’s value to his squad.
“We were talking with the players before in the meeting about how important it is to respect the competition,” he said.
“It’s step by step, little by little; we’re just thinking about the next match. At the moment the main target is the league but we’re really happy.”
Eddie Howe defended making 10 changes for Bournemouth’s edgy 2-1 FA Cup win at Portsmouth, insisting two match-turning substitutions offset the “risk”.
The arrival of Matt Ritchie and Marc Pugh on the hour and Joshua King’s switch through the middle spared Bournemouth’s blushes at Fratton Park as King and Pugh found the net to cancel out Gary Roberts’ first-half goal for the hugely-impressive League Two men.
“We absolutely trust all our players and need to give them chances,” argued Howe.