Martinelli had been in the spotlight following Arsenal's goalless Premier League draw with Liverpool, where he was criticised for attempting to push Conor Bradley back onto the pitch while the defender was injured. Liverpool later confirmed Bradley required knee surgery and would miss the rest of the season.
Martinelli apologised after the match, and Arteta was keen to highlight how the Brazilian answered the situation on the pitch.
"That's personality, coming in and talking on the pitch," Arteta said. "To play for a big club you need a big personality. Sometimes it's a controversial action, sometimes it's a mistake, sometimes it costs you a game. Three days later you play again, so you have to lift yourself up and make it count.
"Today he scored three goals. Tomorrow he'll train a hundred miles an hour. He's not going to change - that's Gabi."
Arteta made 10 changes at Fratton Park, and Arsenal were rocked early when Championship side Portsmouth took the lead after just three minutes through Colby Bishop. The response was swift, with the equaliser arriving five minutes later when Andre Dozzell turned the ball into his own net under pressure from Christian Norgaard at a corner.
Martinelli then took control of the tie, scoring either side of a missed penalty from Noni Madueke to put Arsenal firmly in charge.
"When you make that many changes, cohesion isn't perfect," Arteta added. "We started exactly how we didn't want to, giving them momentum and belief. But once we did the simple things well and became more dominant, the quality showed and the margins grew."
Arsenal's win eased them into the next round, with Martinelli's performance underlining both his quality and resilience.
Darren Fletcher did not hide his frustration after Manchester United were knocked out of the FA Cup, with the caretaker boss hitting out at the referee following a damaging 2-1 defeat by Brighton at Old Trafford on Sunday.
Real Madrid are lining up what has been described as a 'stratospheric offer' for disgruntled Tottenham Hotspur defender Cristian Romero.
Manchester United's problems were further compounded with a 2-1 defeat to Brighton and Hove Albion in the FA Cup third round on Sunday.
Gabriel Martinelli scored a hat-trick as Premier League leaders Arsenal cruised into the fourth round of the FA Cup with a 4-1 defeat of Portsmouth on Sunday afternoon.
