Juve eliminated the Premier League side after a 2-1 victory in their second-leg fixture of the last-16 tie at Wembley Stadium, coming from a goal down on Wednesday evening.
With the Serie A giants advancing with a 4-3 aggregate scoreline, their veteran defender Chiellini conceded it was 'history' and 'experience' that got them through to the next round.
"It's the history of Tottenham," he told BT Sport after the game. "They always created many chances to score so much, but at the end, they miss always something to arrive at the end.
"We believe in the history. I think yesterday and in the first game between Paris [Saint-Germain] and Real [Madrid], the history is important, with experience it's important, and tonight we use our skill and arrive at the win.
"Five years ago, maybe we didn't have this edge, but year after year, you gain it."