Simone Zaza struck the opener for Juve, but Leonardo Blanchard was allowed a free header from a corner in stoppages.
“Am I angry? No, just disappointed," Allegri told Mediaset Premium. “At the end it was only right we conceded on a corner, because we didn't control the situation and shouldn't have given them the chance to equalise.
“It was a mistake to allow Frosinone a corner in the last minute of the game. We tried to do something fancy when we could've just controlled the ball.
“We are paying for this situation with many points in the table now. We have many young players who are unaccustomed to being in a big club and they will learn from these errors.
“Unfortunately at the moment that's who we are – we're capable of beating anyone and losing to anyone."