Captain Mauro Icardi and playmaker Ever Banega both hit hat-tricks as Inter leapfrogged their opponents and moved up to fourth in Serie A.
"This was an exceptional performance where everything we practised worked perfectly," Inter coach Pioli told Mediaset Premium.
"It was a game of a high level and we did well to make it look easy, because Atalanta are a tough opponent and had conceded very few goals until now.
"It was a good result, but what really counts is our position in the table and that means the next match is always the most important.
"We are chasing very, very strong opponents but we have to try to win as many games as possible."
Attention inevitably turned to his two star Argentinians but Pioli was keen to share the credit around.
"Banega played a great match but it is really difficult to find someone who has not played at a high level," he added.
"We think of Icardi, for example, a true champion. The collective has played as a team, showing the desire, determination and mentality to command the game."