Real won 3-2 as Cristiano Ronaldo became the first player to score in every Champions League group stage match.
The holders were set on their way by Borja Mayoral's first goal in the competition, set up by Ronaldo, who quickly added a second himself for his ninth in the competition this season.
Pierre-Emerick Aubameyang struck either side of half-time to unexpectedly level things up but Vazquez's late goal inflicted another defeat on Dortmund.
Zidane said, "It was a good match, with a good start and a good finish, in between it cost us, I am happy for the result, for qualifying and for a match in the Champions League.
"I'm happy for Borja and for Cristiano, in general the team's game, it's not easy when you know you're in the round of 16, against a serious team that played well."
However, Zidane was unhappy with the goals conceded.
"(Keylor Navas) did well, but Keylor and everyone can give a little more."