Federico Chiesa had the Viola ahead with a stunning strike after 12 minutes before Remo Freuler equalised at the 94th minute.
“We contributed with our own errors. Atalanta had a good second half, but it was almost finished, we wasted a great counter-attack with Khouma Babacar and should've have left Freuler unmarked on the edge of the box," Pioli told Mediaset Premium.
“Having said that, we were gritting our teeth and could've won. The refereeing was difficult to accept. I did not see things the same way he did.
“Atalanta were awarded a dubious penalty, whereas the two we weren't given were much less dubious. The tug on Astori and the foul on Dias were clear penalties.
“I judge a referee based on how equally he treats different incidents, so I do not see how it's possible to award one penalty and not the other two, which were far clearer.
“The referees should go on to the field with less pressure, but we've seen that VAR can be used well. Only today Milan were awarded a non-existent penalty against Sampdoria and VAR was used to correct the mistake.
“Atalanta played very well today and we're not saying we were robbed or anything, but a victory would've been very important for our status in the table."