The Greek centre-back found it hard against the Blues in a game where Antonio Rudiger opened the scoring, before a last gasp equaliser from forward Alexandre Lacazette saw the game head to penalties, where the Gunners eventually triumphed.
Sokratis, 30-years-old, is one of new boss Unai Emery's summer signings, with the defender joining for a fee of £17.6m.
The Greek international, along with Stephan Lichtsteiner and Bernd Leno, has been brought in by Emery to sure up the Gunners backline, as defensive errors have been the problem in recent seasons at the Emirates.
With star man Laurent Koscielny still sidelined with injury, it is thought that Sokratis will partner Shkodran Mustafi in the heart of Arsenal's defence come the start of the season. Yet it was this pairing that didn't look comfortable against Chelsea's attack.
Although it is early days for the Greek defender, Arsenal fans were quick to vent their anger, with a number of negative tweets aimed at the summer signing on Twitter:
Bro we bought Sokratis 16m. This guy is terrible— Emery's Son (@donceelogy) August 1, 2018
I think I’d want Cal Chambers starting over Sokratis— Simon Breeze (@Simon_Breeze) August 1, 2018
Mustafi as per usual, shaky... Sokratis still not impressive— LorikF17 (@mo95172) August 1, 2018
Early days, but Sokratis is worrying me a bit!— Hillsy-the-Gooner (@TrevorH18852991) August 1, 2018
Sokratis is livid calm down man you’ve been the worst player— lame (@shutupdec) August 1, 2018
Listen if you had an expectation for Sokratis then I feel sorry for you 😂— Pierre (@j_bonito_) August 1, 2018
With Arsenal's opener against Premier League champions Manchester City coming up on August 12, Emery will be sure to work on his backline and allow Sokratis to flourish as he did at Borussia Dortmund before his move to the Emirates.