The France international has also urged his team-mates to improve as he thinks they were lucky to have won a penalty in the second half.
Spurs drew first blood inside 33 minutes courtesy of a beautiful rabona from Eric Lamela, but Martin Odegaard articulated a response for the hosts on the cusp of halftime.
Arsenal took the lead midway through the second half from the penalty spot through Lacazette after he was brought down inside the area by Davinson Sanchez.
Arsenal are unbeaten in their last ten Premier League home games against Spurs (W6 D4), while Mikel Arteta is the third consecutive Gunners boss to win his first home league meeting with Spurs, following Arsene Wenger and Unai Emery.
"It is amazing. We wanted to win the game for us and the team and the fans. We really missed the fans. It was important to win the derby though,” Lacazette said after the game.
"It was stressful. This is our problem. When we are winning we struggle to manage the game at the end. We need to improve. But we won and now we can think of Thursday. It is important to win this type of game.
"We were lucky to get the penalty, I think. But of course I am happy. Back in the days I have taken a lot of penalties against him [Hugo Lloris] but I was confident
