Bournemouth boss Eddie Howe too inexperienced to manage Gunners, Parlour says.
Santi Cazorla's stoppage-time penalty gave the Gunners the three points.
Arsenal beat Southampton 2-1 in the league.
Paulista is yet to make an appearance for Arsenal in the Premier League this season.
Both teams have won their opening three games.
Alexis Sanchez played a key role in helping Chile win back-to-back Copa America titles.
The injury-plagued midfielder has joined Bournemouth on a season-long loan deal.
The Gunners signed the duo shortly before the transfer window closed.
Iowbi returned to first-team training earlier this week.
Calum Chambers joined Middlesbrough on a season-long loan on transfer deadline day.
Wenger signed Mustafi and Perez in the final week of the summer transfer window.
Mustafi joined the Gunners from Valencia during the summer transfer window.
Arsenal finished second, 10 points behind champions Leicester in the 2015/16 season.
Perez and Mustafi are likely to feature when Arsenal take on Southampton.
Reports have suggested the Cherries boss is being considered as Arsene Wenger's successor.
Aaron Ramsey suffered a hamstring injury during Arsenal's loss to Liverpool.
Alex Iwobi missed the games against Leicester and Watford with a thigh injury.
Chairman Jeff Mostyn says the 38-year-old has 'unfinished business' on the south coast.
Wenger's contract with the Gunners expires next summer.
Alex Iwobi missed games against Leicester and Watford with a thigh injury.
Gunners already tried to sign the Spaniard in January but failed due to the Fifa regulations.
Jack Wilshere has joined Bournemouth on a season-long loan.