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|Arsenal's Brazilian defender David Luiz (centre) controls the ball during the English FA Cup fifth round football match between Portsmouth and Arsenal. (Adrian DENNIS/AFP)|
Mikel Arteta's side desperately needed a morale-boosting success after Olympiakos snatched a late winner to knock them out of the Europa League at the Emirates Stadium on Thursday.
Arteta said his players were still feeling "very down" several days after that kick in the teeth, but they survived an early barrage from third tier Portsmouth to avoid more misery in the FA Cup fifth round.
Sokratis put Arsenal ahead just before half-time and Nketiah bagged the second soon after the interval.
Arsenal's record 13 FA Cup triumphs featured two with Arteta in the team in 2014 and 2015.
The 37-year-old would love to end his first season in charge with another victory lap around Wembley, especially given their hopes of qualifying for the Champions League are hanging in the balance.
"We'll keep going because we love this competition. We're on the right path," Arteta said.
"It's a difficult place to come but I have faith in these kids. They always respond and I always knew they would do that.
"They have to learn from the difficult moments and manage them but they have the talent and desire and look how hard they work."
Arsenal hadn't been knocked out of the FA Cup by a team outside the top two divisions since losing to Wrexham in 1992.
A repeat of that embarrassment would have been a huge blow, so it seemed something of a gamble when Arteta made nine changes against a Portsmouth side who had won 21 of their previous 27 fixtures in all competitions.
Pierre-Emerick Aubameyang and Mesut Ozil were absent, while Alexandre Lacazette and Nicolas Pepe were on the bench.
Pablo Mari made his debut at centre-back after joining on loan from Flamengo in January and David Luiz, Matteo Guendouzi and Lucas Torreira were among the starters.
Torreira lasted less than 15 minutes before the Uruguay midfielder was left writhing in pain after falling awkwardly following James Bolton's tackle.
Referee Mike Dean ruled Bolton's crunching challenge had taken the ball, but Torreira needed four minutes' treatment before being stretchered off while receiving oxygen.
"Lucas was very sore and is in a brace. He will be assessed in a few days and then we will know more," Arteta said.
Portsmouth's fall from grace after winning the FA Cup in 2008 was nothing short of spectacular.
Revived by a 2017 takeover from American billionaire Michael Eisner, who has had stints in charge of Paramount Pictures and Disney, Portsmouth are no longer a 'Mickey Mouse' club.
They are chasing promotion from League One, have reached a second successive Football League Trophy final and tore into Arsenal early on.
Kenny Jackett's side had a glorious chance to take the lead when Steve Seddon's cross picked out Gareth Evans, but he headed wide from 10 yards.
Arteta's team gradually began to impose themselves and Gabriel Martinelli nodded over from close-range after Reiss Nelson's cross curled behind the young Brazilian.
Arsenal made the breakthrough four minutes into first half stoppage-time when Nelson's cross found Sokratis and the Greek defender cushioned a fine volley past Alex Bass from 10 yards.
Buoyed by that confidence boost, Arsenal doubled their lead in the 51st minute when Nelson again caused havoc with a teasing cross.
This time Nketiah was the beneficiary as the 20-year-old's first touch squeezed him between two Portsmouth defenders for a close-range finish that made it three goals in his last five games.
With Portsmouth running out of steam, the two-goal lead was more than enough for Arsenal, whose fourth win in five games would have been even bigger but for Bass's superb save from Bukayo Saka's dipping strike.