Juve - knowing that victory by two goals or more would see them finish on top of UEFA Champions League Group A - could also have been eliminated from the competition on Tuesday.
That could have only occurred if Juve lost and Olympiacos beat Malmo - something they did, 4-2.
Allegri's men dominated the Turin contest, but struggled to convert their possession into clear-cut chances.
In fact, the best chance of the match fell to Atletico, when Koke - sent through on goal - had his sixth-minute effort well saved by veteran goalkeeper Gianluigi Buffon.
A draw was enough for Juve to finish second and reach the last 16 of Europe's premier club competition, leaving Allegri pleased.
"It's always complicated against Atletico, as they defend very well with tight lines, so it's not easy to find passes between the lines," he told Sky Sport Italia.
"Buffon did very well in the first half with a save and we had chances too.
"In the second half we tried to win, but at the same time, not risk losing.
"We didn't want to compromise a qualification I thought was thoroughly deserved.
"Of course we need to improve, as against these big clubs, there are times when you have to defend and protect yourself - something Atletico Madrid do for most of the game."
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