Martinelli was fiercely criticised for trying to push Liverpool defender Conor Bradley off the pitch in the closing stages of Thursday's 0-0 Premier League draw after the Northern Irishman hit the ground with a serious knee injury.
Liverpool confirmed on Sunday the right-back will need surgery and will miss the rest of the season.
Martinelli apologised to Bradley after the game and Arteta hailed his mentality to bounce back in a positive fashion.
"That's personality, come in and talk on the pitch," said Arteta.
"To play for a big club you need a big personality because it can be that (being at the centre of a controversial incident), it can be an action that you miss, it can be something that costs you a game, and three days later there is a game, so you need to lift yourself up and make it count.
"Today he scored three goals, tomorrow he's going to train a hundred miles an hour, for sure. He's not going to change that, that's Gabi."
Arteta had made 10 changes for the clash at Fratton Park and could have been fearing a third round exit for the third consecutive season when the Championship side took the lead after just three minutes through Colby Bishop.
However, the lead lasted just five minutes as the Gunners replied with one of their three goals on the day from corners.
Andre Dozzell turned into his own net under pressure from Christian Norgaard. Martinelli then took centre stage either side of a missed penalty from Noni Madueke.
"When we make that many changes, there is an element of cohesion that is not going to be as perfect as we want," added Arteta.
"We started the game exactly how we didn't want to, giving them momentum and an early goal and hope.
"The more we started to do the simple things right and be a little bit more dominant, the quality took over and the margins were bigger."