Spurs snapped a three-game Premier League losing streak in front of their home supporters.
"What it means for us, the fans... it was important," said Nuno. "It was a hard game and the way we played, the way we responded, it's a big, big moment for us.
"We started well, controlled it, created chances and produced a fantastic goal from Pierre, the way he started and finished the action was really good movement.
"We had something we've improved on, we conceded and we reacted, that's important, because in football you can concede and we made a step forward. There were more goals for us in this game, I feel. We had enough chances to kill the game in our favour.
"Villa are a very good team and they have this weapon of throw-ins and the big guys they put in the box. We did well. It's not about the first contact, it's about how fast you react to the second ball and the boys did really well."