Ziyech was seen strolling in the middle of the pitch after taking a free-kick as Man City counter-attacked and eventually scored through Kevin de Bruyne.
Ilkay Gundogan and Phil Foden were also on target for City during a brilliant first-half performance at Stamford Bridge.
Callum Hudson-Odoi scored a late consolation goal for the hosts but Chelsea nevertheless slipped to a fourth defeat from six games.
Souness told Sky Sports: ‘Just watch Ziyech. He wanders in, watch him! Big players don’t act like that. He needs to sprint back as fast as he can.
‘They don’t stand and watch the game like this. “It’s not my problem, it’s someone else’s problem.”
‘I’m not saying he’s going to race back and make the difference but he needs to get back. Kevin de Bruyne has followed up, he still wants to be part of it.
‘I’m sure when Frank sees that he will point it out to Ziyech that he just cannot do that.’
Souness added: ‘He wasn’t bothered. He didn’t do the basics. He pretends he slips. What does that say about me as a player?
‘I’m not saying he would have prevented the goal but you never know. That must be happening in training and as a manager you have to point it out.
‘In proper teams, that never happens. We’re now in January, he’s been then since the summer. That can’t happen in the big leagues.’
Manchester City’s win seems them climb to fifth in the Premier League, four points behind leaders Liverpool.
City boss Pep Guardiola said: ‘Chelsea one of strongest teams they are suffering from last game but you see the quality of their players and the bench.
‘We cannot play like other teams, we have to play in our rhythm and attack in the right moment.
‘We won titles in that way, more patient. We missed a bit of this tempo and today we had it.’