The Gunners were beaten 1-0 by Pep Guardiola’s side at the Etihad on Saturday thanks to Raheem Sterling’s first-half goal.
Arteta deployed Arsenal summer signing Willian as a false nine for the clash but Cole feels this was ‘disrespectful’ to French forward Lacazette.
The former Manchester United and England striker told talkSPORT: ‘I think he is being disrespectful to Lacazette as well. Willian is not a centre-forward.
‘If you have got a centre-forward on the bench who is your top goalscorer as well, to turn around and say, “Look, I am going to play Willian as the centre-forward. You sit on the bench and watch him play centre-forward”, I think that is very disrespectful.’
Explaining his decision to start Willian and leave Lacazette and Eddie Nketiah on the bench, Arteta said: ‘We need to have the versatility to play in different formations occupying different spaces.
‘It was a game for him, the way City plays and the way they track the opponents and the spaces that can be used.
‘He was really convinced as well. It was obviously really hard to leave two strikers on the bench but it was a tactical decision.’
Arsenal wasted a number of chances as they slipped to a narrow defeat to Man City and Arteta felt his side deserved at least a point.
‘I am upset as I feel we deserved more. I am extremely happy with the performance though, which we put in against a top team,’ he added.
‘I cannot demand more from players apart from we had three chances and had to score.
‘Every goal the opponent scores there is something we can do better, we cannot change that. We know everything has to be perfect in both boxes to beat Manchester City.’