Arsenal were beaten 1-0 by City at the Etihad on Saturday, with Raheem Sterling scoring in the first half.
Lacazette was left out of the Gunners’ starting line-up, with Arteta favouring winger Willian, though the France striker replaced the Brazilian on 69 minutes.
The decision not to start Lacazette irked Cole, however.
“I think he is being disrespectful to Lacazette,” Cole told talkSPORT.
“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.”
After the final whistle, Arteta was questioned about the decision to leave Lacazette out of the starting line-up, and the Spaniard explained: “We need to have the versatility to play in different formations, occupying different spaces.
“It was a game for [Willian], 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.”