The Giallorossi had taken the lead after 90 seconds with a sensational Javier Pastore back-heel flick, crumbled to go 3-1 down and then fought their way back for 3-3.
Di Francesco stated: "We have to give credit to Atalanta, who are in stunning physical form compared to us and indeed many other teams. In the first half they had more fuel in the tank, whereas we got all the distances wrong and were sluggish.
“I would've changed seven or eight players at half-time if I could, but we got it back on track. I got angry again in the last 10 minutes, because we got stretched out and stopped playing as a team again, allowing Atalanta far too many chances to win it.
“We were too bad in the first half to be real. We were slow in our thought process as well as our legs.
"I go crazy because at times I'd like a little more focus. I wanted balance in the last 10 minutes, yet we looked like amateur hour out there with 11 attacking against 11 defending. It's no way to play."