There were chances aplenty in a battle between two of the division's most attacking sides, but neither team could find the breakthrough despite producing a combined 23 shots.
"It's a good draw given how it went. It could have gone either way. It was the right result, it's never easy against Atalanta," Inter captain Handanovic told DAZN.
It was the first time since last January that Inter failed to find the net, a run of 39 league matches. The champions moved two points clear in first place and extended their unbeaten league run to 13 matches, but AC Milan can knock them off top spot by beating Spezia on Monday.
"It is a great result for us, because Inter usually dominate," said Atalanta coach Gian Piero Gasperini. "There were some moments that were in our favour and some not. Both teams wanted to win and that made it a great game."
The hosts missed several players through injury and COVID-19, and faced an Inter team in buoyant form after their imperious league run and midweek Italian Super Cup victory over Juventus.
Inter coach Simone Inzaghi said before the game that he saw Atalanta as a title rival and the match soon lived up to the hype.
Musso produced the first major moment midway through the first half by flying to his right to palm away an Alexis Sanchez shot with his right hand.