The former Manchester City and West Ham United winger praised the club's tenacity but blamed poor defending and a lack of quality in the final third as the main reasons behind the the Scottish champions' failure to win.
He was also quick to suggest that the evening's playing surface - the Rugby Park 3G pitch - was far from ideal.
Celtic were off to a fantastic start within two minutes as Leigh Griffiths tucked away the visitors' opener but Josh Magennis fired their opponents level moments before the break.
Nir Biton's impressive 25-yard effort looked to have given Celtic the win but, after Emilio Izaguirre fouled Greg Kiltie in the penalty area, Kallum Higginbotham chipped home the resulting penalty to ensure a share of the points.
In a game of missed chances, the visiting champions fashioned an impressive 28 attempts at goal - hitting the target with just 12 - while they allowed the hosts 11 efforts at goal in total. So it's clear to see the evidence behind Sinclair's opinion.
With Kilmarnock sitting at the bottom of the Scottish Premiership table prior to kick-off, with zero points to their name, Ronny Deila would have hoped for more at Rugby Park. But Celtic will no doubt dust themselves off and go again, especially with a Champions League play-off upcoming.