The Nerazzurri became the first side to prevent the reigning champions from scoring in a home league game since Udinese in August 2015, with the stalemate enough to see them retain top spot in the table.
They needed the help of the woodwork to pick up a point though, with Mario Mandzukic's first-half header kept out by the crossbar in a game of few chances.
While they barely tested Juve goalkeeper Wojciech Szczesny, Inter's stoic defensive display on their travels is a further indication of the talent in the squad, according to their head coach.
"In the first 20 minutes, we kept the ball well right up to the edge of the area, passing it around nicely," Spalletti said, according to Inter's official website.
"However, in the second half, we lost too many balls considering our quality.
"When you come to this stadium and succeed in keeping a clean sheet and take a point, then it's good. However, we must quickly understand how we've earned a point from an encounter of this calibre thanks to our quality.
"We must be conscious of who and where we are and how we deserve it."
Borja Valero admitted Inter had hoped to carry more of a threat in attack - but were happy enough to take a point back to Milan.
"All of us imagined this match a bit differently, with more goalscoring chances. We did not have many," the Spaniard said.
"We kept the ball well for a long time but didn't manage to threaten, lacking ruthlessness when going forwards.
"However, it must be said that Juventus are a tough team that press a lot. It is difficult to play here.
"Our draw against Napoli and this one helps lift our confidence for what can be an important season for us."