Luca Toni scored the first goal in the new stadium early in the second half on the rebound after Fabio Quagliarella's penalty had been saved by County keeper Rob Burch.
But Martin Allen's League One side ensured their evening became even more memorable when Lee Hughes equalised with a close-range effort three minutes from full-time.
County had travelled to Turin for the once-in-a-lifetime clash at the invitation of the Italian giants, who included the likes of Alessandro Del Piero and Gianluigi Buffon in their starting line-up.
County have made a patchy start to their League One campaign and face a swift return to the reality of lower division life as they prepare to face Walsall at Meadow Lane on Saturday.
The new Juventus Arena is inspired by Premier League stadiums with no running track and the stands designed to be close to the pitch. It was built on the site of the Stadio delle Alpi, the club's previous home.
Juventus switched from their original pink shirts to black and white stripes in 1903 after one of their players, Englishman John Savage, convinced them of County's example.