Juve's American midfielder Weston McKennie missed a simple chance with his head in the opening stages before Napoli went in front through the club's all-time top goalscorer Dries Mertens in the 23rd minute.
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The visitors had chances to add to their lead before the break, but could not find a way past goalkeeper Wojciech Szczesny.
Juve returned for the second half looking like a different side, and got back on level terms through Chiesa in the 54th.
They applied pressure in a bid for the winner but could not create the killer chance, having to settle for a point that leaves them on 35 from 20 games, five points behind Napoli in third and 11 off leaders Inter Milan, who have a game in hand.
"We have to see this in positive terms as a point gained," Allegri told DAZN. "I'd like to see more calm and focus in the final third, but some of it is also to do with the characteristics of the players.
"We have some areas where we need to improve, but overall it was a good performance. We ought to score a few more goals, but we got Chiesa on target, did better with set play situations and had that chance with Weston McKennie, so we're getting there."
There were doubts over whether Napoli would be allowed to travel to Turin for the clash with Juve amid rising COVID-19 cases in the squad, but the local health authority (ASL) granted them permission to make the trip.
Even with several absentees Napoli dominated the opening period, becoming only the second side to fire more than 10 shots at goal in a Serie A first half at Juventus after Lazio in August 2013.
Mertens' first goal since early December, a fizzing strike from the edge of the box, gave the hosts - playing without coach Luciano Spalletti on the touchline after he tested positive for COVID-19 - a deserved halftime lead.
All the goalmouth action happened at the same end early in the second half, as Chiesa drilled just wide before sneaking his effort into the bottom corner via a slight deflection.
Substitute Moise Kean could have snatched all three points for the hosts in stoppage time but headed over leaving Juve still looking for their first league win over a top-four side this season.