A Carlos Tevez double had put the league leaders 2-0 ahead inside the opening 21 minutes, but they were unable to stop a spirited second-half comeback from Verona.
Luca Toni halved the deficit with a trademark header, before Juanito grabbed a point with a 94th-minute effort from a Romulo cross.
Conte was not happy with the way his side had allowed their hosts back into the game, though hopes it will force them to retain their focus for the rest of the campaign.
"It's inexplicable," he said after the disappointing draw. "Matches like these last 95 minutes, and not 45.
"It's not acceptable to be punished by two set plays, we need to be much more certain or we may nullify all the good (work) we have done so far.
"We could've done a lot, lot better. It leaves me perplexed how we could dominate the game for the first half and then end up like this.
"We concede far too many goals from dead ball situations and we've got to be focused, it's a question of concentration.
"It's a shame we drew this game against a Verona side that created few opportunities. I have to compliment them for their determination."
Juve's cushion at the top of Serie A remains five points after Roma were held to a goalless draw by fierce rivals Lazio, but Conte lamented a missed chance to extend their lead.
"Regardless of what the others did, this is a wasted opportunity," he added. "Only we could have let Verona back into the game.
"Let's learn from this and be aware the title isn't won yet. In previous years we won it with determination, aggression and strength. It won't be easy to repeat that."
