Kolasinac, who joined the Gunners from Schalke on a free transfer earlier this summer, started as the left-sided central defender in Arsene Wenger's 3-4-3 formation.
But it was the 24-year-old's role in Leicester's opening goal from a set piece that Neville was most concerned about, labelling the Arsenal defence "naive" and Kolasinac "irresponsible". But Danny Welbeck levelled before the break.
Craig Shakespeare has opted to leave new signing Kelechi Iheanacho on the bench, although supposed Roma target Riyad Mahrez features in a starting XI that also includes Jamie Vardy and Shinji Okazaki.
Mourinho predicts seven-way fight for Premier League title
But for the beginning of the season, we lost some important ones too: Rojo, Young, Shaw, Zlatan, players with injuries. But we are involved in four competitions.
"I have to say, their new centre-back, it's so irresponsible what he does", says Neville on Sky Sports.
"For us it was a bit disappointing with the goals that we've let in and we shouldn't really be conceding in that way, but I think we showed great determination and great togetherness to get back into the game and we won it towards the end of the game".