Spurs conceded a stoppage-time equaliser against West Brom on Saturday to prolong Villas-Boas' search for his first victory in charge of the north London club.
The 34-year-old is under pressure to restore his reputation in English football after being sacked at Chelsea in March, and his team's lack of ruthlessness in front of goal cost him against the Baggies.
But Assou-Ekotto said: "He's cool. He has a different way to work, so we learn different things from him.
"He's like the son of Mourinho because he used to work with him and he works in the same style. We do a little more tactics at training.
"If we work more about tactics we can win and we will enjoy (our football).
"We didn't do enough to win, but it's only a matter of small details," the left-back said. "If we fix these details, we will be perfect for the next game."
- West Brom