The former Manchester United captain believes Ozil "bottled it" when Willy Caballero beat him to the ball in a second-half opportunity.
Neville also slammed Koscielny for failing to battle on after suffering an injury prior to his half-time substitution and criticised Walcott for his negative reaction to being substituted for Olivier Giroud midway through the second period.
Sunday's draw at the Emirates Stadium left Arsenal sixth in the Premier League table, seven points behind City, and Neville felt the trio should take their share of the blame.
Pundit Neville said to Sky Sports: "Arsene Wenger has touched on the chance Mesut Ozil had and I might be being a bit harsh with three things here, but I'm going to say them anyway.
"Mesut Ozil goes through on goal and bottles out of a challenge when his manager's backside is on the line. Go for a 50-50 or nick in front and get the penalty – win the ball.
"Mesut Ozil should go for a 50-50 with the goalkeeper. That would help, wouldn't it?
"Koscielny – he always goes off. He is a centre-back. He plays to half-time and then goes off.
"He might have a bit of a problem with his Achilles and I might be being very harsh, but he went off against Bayern Munich and went off in this big game.
"Arsene Wenger deserved for Koscielny to at least have a go for five minutes in the second half. 'Go on mate, have a go for us'. No, he didn't.
"Walcott trudges off the pitch. He hasn't played well, but his attitude is, 'I have scored a goal, you shouldn't take me off.' Yes you should, because you were poor and that is a matter of fact.
"Theo Walcott should sprint off the pitch and shake the manager's hand and say, 'Thanks very much for giving me a game today. I'm lucky'.
"There is three instances and I'm being harsh, but if you are talking about throwing the cat among the pigeons, let's do it. Let's throw it out there."