The first-choice trio of Laurent Koscielny, Nacho Monreal and Sead Kolasinac remain injured ahead of Wednesday's trip to Stamford Bridge with none of the three to have featured this year.
Arsenal midfielder Jack Wilshere is a doubt for this weekend's clash with Bournemouth after limping out of the Gunners' game with Chelsea.
Alexis Sanchez was left on the bench amid relentless speculation over his future, though, and Arsenal could have perhaps done with the Chilean on the field during a subdued start to the match.
Eden Hazard recovered from a calf complaint to start for Chelsea and the Belgium star played in Morata after two minutes, although the angle was against the striker - who endured a torrid outing when the sides met in the league last week - and he shot into the side netting.
Moses then went close for Chelsea with a low shot destined for the back of the net only to see effort deflected over by Shkodran Mustafi.
Andreas Christensen should have had the opener soon after half-time, but he somehow managed to put his back-post header over the bar after a fine flick-on from a set piece.
Wenger has separately been asked for his observations for comments made both before and after Arsenal's 2-2 draw with Chelsea on Wednesday night, for which he has until Tuesday 9 January to respond, and could face further punishment.
Chelsea, meanwhile, are also aiming to bounce back after their goalless draw with Norwich in the third round on Saturday.