Danilo struck late for Juventus to cancel out Ruslan Malinovskyi's opener.
“It would've been disappointing to lose a game after playing so well," Allegri told DAZN.
“We made mistakes in our finishing and the final ball, there were three minutes of terror just before half-time on the counter after we lost the ball cheaply and De Ligt threw himself in the way twice.
“The second half was better, paradoxically when we were meant to score, we got the pass wrong, Atalanta were on the counter and Malinovskyi did well to win that free kick. It was an extraordinary goal and Danilo scored a great equaliser.
“Atalanta are very aggressive, so we had to move the ball quickly to get it behind them. It was a very entertaining game, we were losing 1-0 and risked defeat, but it is an important point. We wanted to win, but knew Atalanta were strong and so we're happy to keep the unbeaten run going."
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