Milan Skriniar struck the winner early into the second-half.
“We expected a difficult match because Atalanta are an excellent team," Handanovic told Sky Italia.
“They are showing it both in Italy and in Europe, they are not easy to play against. I think it was a game where we suffered a bit, but we still win this way."
The veteran shot stopper admitted it was tough bot 'physically and tactically', but was content the team got away with a clean sheet and three points.
“The details decide these games," he said. “They were dangerous in the first half but we were good and lucky not to concede and then we did it.
“It was a tough game, physically and tactically. The important thing is to always win because all of the matches are worth three points.
“This was an important win for the championship. The other teams will also play against Atalanta, who are not an easy opponent."